Part 1: Equations

1. Draw the following graphs:

a. Y = 4X - 2 b. Z = 2/X - 10 c. 8X -4Y = 10

2. The demand for electricity (Qd) in any municipality is dependent upon the price of electricity (P), the population (POP), and median income (Y).

• a. Assume that the demand function is linear in all the variables and construct an equation for the demand function.
• b. describe the expected restrictions on the parameters in the equation based on your knowledge of economic theory
• c. Assume that a study of demand for electricity has found demand to be higher in Providence than Hartford but that in Hartford demand is more responsive to price changes. Draw on one diagram the two demand curves.

3. The balance of trade problems and the breakdown of GATT's Uruguay Round of trade talks has focused attention on the demand for imports. A recent econometric study of import spending in the US has produced the following equation:

M = 6100 - 2.1*CPI + .25*Y

where Y = income

CPI = price level

• a. Are the signs on the coefficients what you would expect? Explain.
• b. How would the import demand equation for Canada differ if import demand were more sensitive to changes in income in Canada;
• c. Draw on one graph the curves relating import demand (M) to Income(Y) for the two countries.

4. You are to assume that the cost of public services, police, fire, education... (C), increases proportionally with the size of the population (P) and that the revenues from taxes are proportional to the taxable real estate base (B), the proportion being the real estate tax rate (t). You are to use this information to derive the equation for the tax rate and determine what will happen to the property tax if there is an increase in the population greater than the increase in the amount of taxable property?

5. Below you will find a number of behavioral equations. I want you to identify the parameters in each equation so that you can determine how the following behavioral changes will show up in the equations. More specifically, you are to determine how the following changes will be reflected in changes in the parameters.

Where

C = consumption YD = disposable income

I = investment r = interest rate

P = price QD = demand

K = income M= money demand

p = inflation U = unemployment

• a. An increase in the sensitivity of investment spending to interest rates.
• b. An increase in the sensitivity of money demand to interest rate changes.
• c. A decrease in investment spending.
• d. A decrease in the sensitivity of unemployment to the inflation rate.
• e. An increase in the income elasticity of demand.
• f. A decrease in demand for money.

6. The cost (c) of truck transportation depends upon the gas and maintenance of the vehicle and the salary of the driver. The cost of operating a truck (excluding the cost of the driver) is dependent on the speed(s) of the truck. This fixed cost is $5 and the cost increases by $.50 for every one mile/hour increase in the speed. The driver's salary is $6 per hour.

• a. Assuming the trip is 300 miles, you are to derive the function relating the total operating cost to the speed of the trip. Hint: To do this, begin by developing two separate cost functions - one for the driver's expense, and one for the gas and maintenance.
• b. Assuming the legal limits to speed are 40-70 mph, what speed should the driver drive if he/she is concerned with minimizing cost?

7. The personnel director for Electronics Associates developed the following estimated regression equation relating an employee's score on a job satisfaction test to his or her length of service and wage rate:

y - 14.4 - 8.69Xl + 13 5X2

where:

Xl - length of service (years)

X2 - wage rate (dollars)

y - job satisfaction test score (higher scores indicate more job satisfaction)

• a. Interpret the coefficients in this estimated regression equation.
• b. Develop an estimate of the job satisfaction test score for an employee that has 4 years of service and makes $6.50 per hour.

8. The three equations below are segments of the estimated demand equations for motor vehicles, furniture, and food.

lnQ1 = .718lnY + .534lnY-1 + .355lnY-2 + .178lnY-3 - .398lnP

R2 = .56

lnQ2 = .156lnY + .116lnY-1 + ..077lnY-2 + .039lnY-3 -.596lnP

R2 = .89

lnQ3 = .531lnY + .398lnY-1 + .265lnY-2 + .133lnY-3 - .334lnP

R2 = .76

where:

Q = quantity demanded Y = income

P = price -1 = lagged one period

• a. Identify the equations and briefly describe the basis for your selection. (Ex. Do you believe that the first equation would most likely be the food, furniture, or automobile equation?)
• b. Use your answer to part a to describe the differential behavior of industry sales over the business cycle.
• c. If income falls 2 percent in 1991, 1.5 percent in 1992, and rises 1 percent in 1993, how much will demand have changed for Q2 from its present level if no other changes take place?
• d. How much would the supplier of good 3 need to lower the price to keep sales constant next period in the face of a 3 percent expected decline in income?

9. Suppose you have estimated the following demand function:

Qn = 10.3 - 3.1Pn -2.00Y + 1.50Pr

where:

Qn = quantity of good n Pn = price of good n

Pr = price of good r Y = household income

Assume that Pn = 300, Y = 1000, and Pr = 200.

• a. Are the two goods complements or substitutes?
• b. What will happen to the revenue from selling good n if the price does not change in response to a 10% drop in the price of good r?
• c. What is the value for the own price elasticity?
• d. Should the producer raise, lower, or keep unchanged the price of N if its objective is to maximize revenue in the face of the drop in the price of R?

10. The demand for XZY personal computers can be characterized by the following demand equation:

Qd(X) = PX-2PA1.87Y2.3.

The demand for ABC computers can be characterized by the following demand equation:

Qd(A) = 100 -2.4PA +3.4PX +4.5Y

If price of ABC= PA, price of XYZ=PX, and Income=Y

• a. How much will Qd(X) change if the computer's price is raised 5%? How much will Qd(A) change if the computer's price is raised by 5%?
• b. How much will demand change for both computers if the economy falls into a recession and income declines 3.5%?

1. The private sector supply and demand for gold are given by the following equations:

• a. Solve for the equilibrium price.
• b. Solve for the equilibrium price if the government pays all buyers a subsidy of $5 per unit of gold.

2. A student in ECN 125 has a problem (you think you have it bad). They have two exams on next Friday - one in ECN 125 and one in HIS 180. The difficulty they face is allocating their study time between the two courses. You have to decide what possibilities they have with the following information

• there are ten hours of study time available
• in both courses, you get a zero with no time spent studying
• for each hour spent in the study of economics, your grade increases eight points
• for each hour spent in the study of history, your grade increases seven points
• a. Draw the grade possibility curve (the maximum grade possibilities assuming full use of the time.
• b. What is the cost of a ten point improvement in your economics grade?
• c. Now assume that you realize that there are advantages to working together. If you study for ECN 125 together, this person will find that for each hour spent in studying the subject, the grade increases by 9.5 points. What is the new grade possibility curve?
• d. What is the cost of a five point increase in the history course?
• e. Derive the equation for the 'grade production functions' and the 'grade possibility' curve. Be sure to specify all the 'bits' of information that are used in the construction of this equation.

3. The price of gold, like all other market prices, is determined by the interaction of supply and demand. The demand curves for the OPEC countries ( QDO), the non-OPEC central governments (QDG) and the non- OPEC private sector (QDP) are given below:

• a. Calculate the aggregate demand curve for gold.
• b. Assume that the momentary supply is fixed at 500. Determine the equilibrium price and consumption level for each group.
• c. Assume that the long-run supply curve goes through the equilibrium point in (b) and for every one unit increase in price there is a one unit increase in supply. Derive the equation for the long-run supply curve.

d. Calculate the long-run and short-run equilibrium values for P and Q if there is an outward shift in the OPEC demand curve of 200 units

4a. There has been a rather heated debate between monetarists and Keynesians over the proper role of fiscal and monetary policy since the 1930s. In your ECN125 and ECN327 classes you used simple models to look at how the economy responds to both fiscal and monetary shocks. The first, and by far the easiest model, is the simple income determination model of the macro economy. To help you the following information is being supplied.

1. consumption (C) is a linear function of income (Y)

2. disposable income (D) equals income less taxes (T)

3. investment (I) and government (G) spending are exogenously determined

4. taxes are a linear function of income

5. aggregate demand (AD) is equal to the sum of consumption, investment, and

government spending) The economy is in equilibrium when income equals aggregate demand

• With this set of relationships you are to answer the following questions.
• a. Construct the set of equations that describe this model
• b. Identify the behavioral and equilibrium equations and any identities
• c. Solve for the reduced form equation for income
• d. What is the value of the government multiplier?
• e. What parameters influence the size of the multiplier? For example, what happens to the multiplier when the income tax rate is increased.

4b. The Reagan presidency will be remembered for many things, but high on the list will certainly be the budget deficit. During his presidency, as a result of numerous deficits exceeding $100 million, the national debt more than doubled Deficits are the result of both structural and cyclical factors. To demonstrate the impact of cyclical movements of the economy on the deficit, I want you to build a simple macro model. The assumptions you are to make are:

A. Aggregate demand(AD) is the sum of consumption(C), investment(I), and government(G) spending;

B. Consumption is a linear function of disposable income(YD);

C. Taxes(T) are a linear function of income(Y);

D. In equilibrium aggregate demand equals income, and;

E. Investment and government spending are exogenously determined.

With this information you are to answer the following questions:

• a. Set up the equation of the model;
• b. Identify the endogenous and exogenous variables and the parameters in the model (be sure there are enough equations to solve for each of the endogenous variables);
• c. Specify reasonable ranges for the parameter values;
• d. Solve for the equilibrium level of output;
• e. Solve for the reduced form equation for the budget deficit;
• f. How does the budget deficit respond to a change in the level of investment spending? Be specific, use the model and be sure to explain the results.

4c. George Bush's presidency inherited a significant international trade deficit from the Reagan years. As a result of many government budget deficits exceeding $100 million, U.S. international indebtedness more than doubled. Trade deficits are the result of both structural and cyclical factors. To demonstrate this I want you to build a simple macro model. The assumptions you are to make are:

A. Imports(I) are a linear function of disposable income(YD);

B. Aggregate demand(AD) is the sum of consumption(C), investment(I), government(G), and export(X) spending minus import(M) spending;

C. Consumption is a linear function of disposable income(YD);

D. In equilibrium aggregate demand equals income;

E. Investment, exports, government spending, and taxes(T) are exogenously determined.

You are to do the following:

• a. Set up the equation of the model.
• b. Identify the endogenous and exogenous variables and the parameters in the model. (Be sure there are enough equations to solve for each of the endogenous variables).
• c. Specify reasonable ranges for the parameter values.
• d. Solve for the equilibrium level of output.
• e. Solve for the reduced form equation for the trade deficit.
• f. How does the trade deficit respond to a change in the level of government spending? (Be specific, use the model and be sure to explain the results).

Index