Category: Economics

Short-run versus long-run costs and expenditures
The following graph shows isoquants for the technologically efficient bundles of labor and capital for producing 100 and 200 units of output (labeled q=100 and q=200, respectively). Suppose the firm is initially using the cost-minimizing bundle of labor and capital for producing 100 units of output, represented by point A.
Assume that the expansion path is a straight line in this case. Use the grey line (star symbol) to show the expansion path for this firm on the graph.
Complete the following table by entering the total amount the firm would have to spend on capital and labor at each level of production in both the short run and the long run if the wage rate (w) is $20 and rental rate of capital (r) is $40.
Quantity Produced
Short-Run Costs (Dollars)
Long-Run Costs (Dollars)
0
100
200
The following graph is intended to help you answer the question that follows.
First, use the orange points (square symbols) to plot the total long-run costs when producing 0, 100, and 200 units of output. Then, use the blue points (circle symbols) to plot the total short-run costs associated with producing 0, 100, and 200 units of output.
Note: Select and drag the curve from the palette to the graph. To move a point on the curve, select and drag to the desired position. You will not be graded on your placement of any objects on the graph.
Long-run Costs
Short-run Costs
True or False: According to this graph, the firm’s long-run costs are never higher than its short-run costs.
True
False

Consider an overlapping generations model in which agents live two periods. Each agent inelastically supplies one unit of labour services when young. For an agent born in period t, utility is given by:
Ut = c1t1-θ1-θ + (1/(1+ρ)) c2t+1 1-θ
where c1t is consumption when young, c2t+1 is consumption when old, 0<ρ<1 is the rate of time preference, and θ>0 is a parameter. The agent’s budget constraint in each period of life are given by:
st + c1t = wt (1 – τt),
c2t+1 = (1 + rt+1) st
where st is savings when young, wt is the wage rate, τt is the tax rate on wages, and rt+1. The production function is:
Yt = A Ktα Lt1-α
where A is a fixed parameter representing technology, Kt is the aggregate capital stock, and Lt is the number of workers, equivalently the population of the young generation. To simplify, assume that population is fixed over time. The government spends all of its tax revenue each period such that:
Gt = Lt wt τt
Derive the Euler equation relating consumption when old to consumption when young as a function of the interest rate. Interpret θ – 1.
B.
Now, set θ = 1, and solve for the consumption in both periods and for savings as a function of the wage rate and the interest rate. Does saving depend on the interest rate? Explain in terms of income and substitution effects.
C.
Assume perfectly competitive markets, write expression for the real wage rate and the interest rate. Use these results to solve for the reduced form for the steady-state stock of capital.
D.
How does increase in government spending affect the capital stock? Compare the effects in the OLG model with those of representative agent Ramsey model. Explain.

A two-period extraction example:
You’re working as an economist at a mining firm.This firm has just obtained a 2-year lease on a cobalt mine which has a fixed stock of 9,000 metric tons (MT) of cobalt available. It is your job to determine the optimal extraction path over the length of the lease for this firm. In other words, you need to determine how much the firm should extract in year one (q1) and in year two (q2). The firm receives a fixed price for its cobalt of$3,000/MT and faces marginal costs of extraction MC = 400 0.5q. The discount rate is 10% (r= 0.1). Use the two-way graph below to answer the following questions (you may redraw this graph if you need to).
a. Derive the year 1 marginal net benefits function (MNB1) and the year 2 present value marginal net benefits function (PVMNB2). Plot these functions on the two-way graph above. Be sure to label the axis intercepts and show your work below.
Does the stock constraint bind in this case? Show your work below.
c. What is the optimal extraction decision for this firm? Show your work below and indicate the optimal choice of qi and q on the graph above.
d. The EPA has determined that there are external costs associated with the extraction of cobalt and has estimated that these costs are $350 per metric ton of cobalt extracted. If the firm is made to account for these external costs, what direction will that shift the MNB1 and PVMNB2 curves? Use the two-way graph to illustrate.
e. What is the firm’s new, socially efficient extraction plan? How does this compare to your answer in part c? Show your work below.

Using a dataset on SAT scores, class size and demographic characteristics of a sample of students, the following model is estimated:
sat = β0 + β1 ⋅ hsize + β2 ⋅ hsize^2 + β3 ⋅ female + β4 ⋅ black + β5 ⋅ (female ⋅ black)
sat = 1028.09 + 19.29 ⋅ hsize − 2.19 ⋅ hsize^2 − 45.09 ⋅ female + 169.81 ⋅ black + 62.30 ⋅ (female ⋅ black)
(Standard errors in parentheses: (12.713) (6.29) (3.832) (0.527) (18.154) (4.291))
Where:
sat: combined SAT score
hsize: size of student’s high school graduating class (in hundreds)
female: dummy variable for gender (1 = female)
black: dummy variable for race (1 = Black)
(a) Is there strong evidence that hsize should be included in the model?
(b) Holding hsize fixed, what is the estimated difference in SAT score between nonblack females and nonblack males? How statistically significant is this estimated difference?
(c) What is the estimated difference in SAT score between black males and nonblack males? How statistically significant is this estimated difference?
(d) What is the estimated difference in SAT score between black females and nonblack females? (Hint: plug in values for black and female to get the required group)

HELPP!! Regulating a natural monopoly
Consider the local telephone company, a natural monopoly. The following graph shows the demand curve for phone services, the company’s marginalrevenue curve (labeled MR), its marginal cost curve (labeled MC), and its average cost curve (labeled AC). (Hint: Select a point on the graph to seeIts exact coordinates.)
Assume no government regulation. If the natural monopoly provides the profit-maximizing output, it will provide phone services tohouseholds per month at a price of
Suppose that the government forces the monopolist to set the price equal to marginal cost. In the short run, under a marginal-cost pricing regulation,the monopolist will provide phone services tohouseholds per month at a price of
If the government forces the natural monopoly to set its price equal to marginal cost, how will the company react in the long run?
Because the firm earns a profit under marginal-cost pricing, it will remain in the industry in the long run.
Because the firm suffers an economic loss under marginal-cost pricing, it will reduce its output to 3,500 households per month in the longrun.
Because the firm suffers an economic loss under marginal-cost pricing, it will exit the industry in the long run.
Suppose that the government forces the natural monopoly to set its price equal to average cost. Under an average-cost pricing policy, the monopolistwould provide phone services tohouseholds per month at a price ofand earn a profit ofper month.
True or False: Over time, the telephone company has a very strong incentive to lower costs when subject to average-cost pricing regulations.
True False