# BEO2264 Microeconomics Analysis: Production Function

### Questions:

A furniture manufacturer is producing in the short run with one fixed input, capital. The manufacturer has recorded the following levels of units output corresponding to different numbers of units if labour.

 Number of units of Labor Number of Units of Output 1 10 2 18 3 24 4 28 5 30 6 28 7 25
1. Calculate the marginal and average product of labor for this production function.
2. Does this production function exhibit diminishing returns to labor? Explain.
3. Explain what might cause the marginal product of labor to become negative.

It has been advised to invest in a coffee house produces coffee under the production function q = 5KL, where q is the number of cups generated per hour, K is the number of coffee machines (capital), and L is the number of employees hired per hour (labour).

1. What is the average product of labor?
2. What is the marginal product of labor?
3. The average product of labor and the marginal product of labor are both equal to AP = MP = 5K.

Does labor exhibit Diminishing Marginal Returns in this case?

A firm’s total cost function is given by the equation:

TC = 4000 + 5Q + 10Q2.

Write an expression for each of the following cost concepts:

1. Total Fixed Cost
2. Average Fixed Cost
3. Total Variable Cost
4. Average Variable Cost
5. Average Total Cost
6. Marginal Cost
7. Determine the quantity that minimizes Average Total Cost. Demonstrate that the predicted relationship between marginal cost and average cost holds.The market for rice consists of 500 identical firms, each with the total and marginal cost functions shown:

TC = 90,000 + 0.00001Q2

MC = 0.00002Q

where Q is measured in tons per year. The market demand curve for rice is

Q = 90,000,000 – 20,000,000P

where Q is again measured in tons and P is the price per ton

1. Determine the short-run equilibrium price and quantity that would exist in the market.
2. Calculate the profit maximizing quantity for the individual firm. Calculate the firm’s short-run profit /loss at that quantity.

The total and marginal cost functions for a typical mining manufacturer are:

TC = 75,000 + 0.1Q2 and MC = 0.2Q

where Q is number of loaded cars per year.

The industry consists of 55 identical producers.

The market demand curve is:

QD = 140,000 – 425P

where P is the price per carload.  The market can be regarded as competitive.

1. Calculate the short run equilibrium price and quantity in the market. Calculate the quantity that each firm would produce.
2. Calculate producer surplus, consumer surplus, and total surplus at the equilibrium values.
3. Calculate the firm’s profit or loss.

The industry demand curve for a TV market is:

Q = 1800 – 200P.

The industry exhibits constant long-run average cost at all levels of output, regardless of the market structure. Long-run average cost is a constant \$1.50 per unit of output.

Calculate market output, price (if applicable), consumer surplus, and producer surplus (profit) for each of the scenarios below

1. Perfect Competition
2. First Degree Price Discrimination

The soft gadget market is controlled by two firms: Acme and Widgetway. The structure of the market makes secret price cutting impossible. Each firm announces a price at the beginning of the time period and sells drinks at the price for the duration of the period. There is very little brand loyalty among buyers so that each firm’s demand is highly elastic. Each firm’s prices are very sensitive to inter-firm price differentials. The two firms must choose between a high and low-price strategy for the coming period. Profits (measured in thousands of dollars) for the two firms under each price strategy are given in the payoff matrix below. Widgetway profit is before the comma; Acme is after the comma.

Does either firm have a dominant strategy? What strategy should each firm follow?

1. Assume that the game is to be played an infinite number of times. (Or, equivalently, imagine that neither firm knows for certain when rounds of the game will end, so there is always a positive chance that another round is to be played after the present one.) Would the tit-for-tat strategy be a reasonable choice?  Explain this strategy.
2. Assume that the game is to be played a very large (but finite) number of times. What is the appropriate strategy if both firms are always rational?