03 Jun Question 2. Consider estimation of a short-run avera
Question
2. Consider estimation of a short-run average .yariable cost function of the form:
Ave = a + bQ + cd
Using time-series data, the estimation procedure produces the following computer output:
VARIABLE
INTERCEPT
PARAMETER STANDARD
ESTIMATE ERROR
7.5 26.5
-0.0120 0.0058
0.00006 0.000013
T-RATIO
2.83
-2.07
4.62
P-VALUE
0.0107
0.0524
0.0002
DEPENDENT VARIABLE: AVe
OBSERVATIONS: 22
R-SOUARE F-RATIO P-VALUE ON F
0.8557 56.32 0.0001
o
02
a. Average variable cost reaches its minimum at what level of output? What is minimum average variable cost at this level of output?
b. When output is 6,000 units, what is average variable cost and marginal cost?
3. The table below shows a perfectly competitive firm’s short-n;n production function. Labor is the firm’s only variable input, and the market price for the firm’s product is $2 per unit.
Units of Labor Units of Output
3
4
5
6
7
370
490
570
600
620
a. How much does the fifth unit of labor add to the firm’s total revenue?
b. If the wage rate if $200; how many units oflabor will the firm emplc y?
c. How many units of labor will the firm employ at a wage rate of $200 if the market price fort he firm’s product increases to $5?
4. A consulting company in a perfectly competitive industry fo recasts the market price for the next year to be $6.
Average variable cost is estimated to be:
Ave = 14 – O.008Q + o.ooooozo’
Total fixed cost will be $6,000 next year.
a. Should the firm produce or shut down next year? Explain.
b. If the firm produces next year what will be the profit-maxim: zing output choice?
c. What will the firm’s expected profit (loss) be?
5. A monopoly firm faces the following estimated demand and average variable cost functions:
Qd = 100,000 – 500 P + 2M + 5000 PR
AVe = 520 – 0.03Q + O.OOOOOlg
Where Qd is quantity demanded, P is price, M is income, and PR is the price of a related good. The manager has forecasted the values of M and PR will be $50,000 and $20, respectively, in 2014. Total fixed cost in 2014 is expected to be $4 mill.on.
a. . Should the manager produce or shut down in 20l4? Explain.
b. If the firm operates in 2014, what will be the profit-maximizing price and output?
c. What will the firm’s expected profit be?
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