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# TP, MP, and AP Equations

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1) A firm estimates its long-run production function to be Q= -0.0075K3L3 + 12K2L2. If the firm fixes its K use at 12 units, what are this firm's TP, MP, and AP equations?

2) Suppose a firm's TVC function is TVC = 96Q - 2Q2 + 0.05Q3
a. What is this firm's AVC equation?
b. What is this firm's MC equation?
c. Theory predicts that MC equals AVC when AVC is at its minimum. Compute the value of Q when AVC is at its minimum, and check the accuracy of the prediction of this theory

3) Determine whether each statement given below is true or false and explain your answer in no more than 2 sentences.
a. A perfectly competitive firm has no incentive to raise or lower price to increase sales.
b. In an increasing- cost industry, output expansion will in the long run lead to a decrease in industry output and an increase in market price.
c. Unlike a perfectly competitive firm, an oligopolistic firm can continue to earn excess economic profit in the long-run.
d. If firms operating in a perfectly competitive market are currently earning excess economic profit, the market supply will decrease and the market price will increase in the long-run equilibrium.

4) A company is considering between two projects: project 1 and project 2. The estimated cash flows and their probabilities of the two projects are given below.

Project 1 Project 2
Cash inflow Probability Cash inflow Probability
\$3,000 0.10 \$2,000 0.10
4,000 0.20 3,500 0.25
5,000 0.40 5,000 0.30
6,000 0.20 6,500 0.25
7,000 0.10 8,000 0.10
a. Calculate the expected value (revenue) from each project.
b. The variances of project 1 and project 2 are 1,200,000 and 2,925,000, respectively. Calculate the coefficient of variation of each project.
c. Based on the coefficients of variation you computed in b above, determine which project the company should choose.

5) Suppose a manager faces the following cost, price, and total revenue functions for a steak lunch meals in a theme park restaurant.
TC = 5Q + 0.02Q2
P = 20 -0.05Q
TR = 20Q - 0.05Q2
Where, Q = number of steaks served in a day.
a. What is the optimal number of steaks served?
b. What is the price that the manager charges for a steak?
c. What is the daily profit earned from steak lunches?

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#### Solution Summary

TP, MP, and AP equations?

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## Questions about Cubic Production Function: What are the equations for total product, average product, and marginal product? When does marginal product of labor begin to diminish? What is average variable cost and marginal cost?

In Microsoft Excel please respond to all questions and math problems in the following problem (See Attachment). Please show Microsoft Excel formula(s) and work.

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Homework Exercise Numbers 1

1. A firm estimates its cubic production function of the following form: Q = AL3 + BL2 and obtains the following results:

[see attachment for table]

a. The equations for total product, average product, and marginal product are:
TP = ___________________________
AP = ___________________________
MP = ___________________________

b. The estimated values of A and B are statistically significant at the (exact) levels, ________ and _________, respectively.

c. At _______ units of labor usage, marginal product of labor begins to diminish.

When the wage rate is \$300, answer the following questions. (Remember that AP =
Q/L; AVC = w/AP; and SMC = w/MP.)

d. Average product of labor reaches its maximum value at ________ units of labor.

e. At the output for part d, average variable cost is \$______________ and marginal cost is \$____________.

f. When the rate of labor usage is 100 units of labor, output is _______ units.
Average variable cost is \$_________ and marginal cost is \$__________.

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