Problem 1
(a) What information does the production function provide? (b) Explain why the production function does not provide enough information for anyone actually to runa firm
Problem 2
(a) Calculate the marginal and average costs for each level of output from the following total cost data. (b) Show how marginal and average costs are related. (c) Are these short-run or long-run cost curves? Explain how you can tell. $$ \begin{array}{|l|l|l|l|l|r|r|r|r|r|r|} \hline \text { Oulput } & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline \text { TC }[\underline{f}) & 12 & 27 & 40 & 51 & 60 & 70 & 80 & 91 & 104 & 120 \\ \hline \end{array} $$
Problem 3
(a)Explain why it might make sense for a firm to produce goods that it can only sell at a loss. (b) Can it keep on doing this forever? Explain.
Problem 4
Common fallacies Why are these statements wrong? (a) Firms making losses should quit at once. (b) Big firms can always produce more cheaply than smaller firms can. (c) Small-scale production is always better.
Problem 5
The table below shows how output changes as inputs change for three different output levels. The wage rate is \(£ 5\) and the rental rate of capital is \(£ 2\). $$ \begin{array}{|l|l|l|c|c|l|c|} \hline & \text { Column } 1 & \text { Column } 2 & \text { Column } 3 & \text { Column } 4 & \text { Column } 5 & \text { Column } 6 \\ \hline \text { Caplral input } & 4 & 2 & 7 & 4 & 11 & 8 \\ \hline \text { Labour input } & 5 & 6 & 10 & 12 & 15 & 16 \\ \hline \text { Output } & 4 & 4 & 8 & 8 & 12 & 12 \\ \hline \end{array} $$ a. For each output level in the above table, which technique of production is more capital intensive? b. Refer to columns 2,3 and 6 . Does the firm switch towards or away from more capital-intensive techniques as output rises?
Problem 6
For each of the following cases explain how long you think the short run is: a) a power station; (b) a hypermarket; (c) a small grocery retail business. In explaining your answer, specify any assumptions you need to make. For each case, do you expect the law of diminishing marginal returns to hold?
Problem 8
The marginal cost of supplying another unit of output of an electronic product via the Internet is almost zero. If long-run equilibrium means price equals marginal cost, all Internet firms will go bust. Can you resolve this situation?
Problem 9
What kind of returns to scale do the following production functions display? (a) \(Q=\sqrt{K L}\) (b) \(Q=K_{0.3} L_{0.2}\) (c) \(Q=K+L\)
Problem 12
Suppose that firm \(\mathrm{A}\) has the following short-run production function \(\mathrm{Q}=\mathrm{K}_{\mathrm{c}} \sqrt{\mathrm{L}}\), where \(K\) denotes capital and \(L\) labour. Suppose that the level of capital is fixed at \(\mathrm{k}_{0}=10\) The total cost of firm \(\mathrm{A}\) in the short run is \(\mathrm{STC}=10 \mathrm{wL}\) where \(w\) is the wage paid to each worker. Assume that the wage is \(£ 20\). Using the production function, show how the short-run total cost depends on the quantity produced \(Q\). Plot the short-run total cost on a graph, where you put \(Q\) on the horizontal axis.
Problem 13
The following table shows data about quantity produced and total cost of production in the long run for a given firm: Find the long-run marginal cost and the long-run average cost faced by the firm. On a graph, plot the \(L M C\) and \(L A C\) curves. Explain why the \(L M C\) curve cuts the \(L A C\) curve from below.
