Macroecon 3

3. The short-run cost function of a firm is given by C(q) = 200 + 55q, where C(q) or T C(q) is total cost, and q is the total quantity of output, both measured in thousands.

(a) What is the company's fixed cost?

(b) If the company produced 100 (in thousands), what would be its average variable cost? What is the average variable cost as a function of q?

(c) What is the marginal cost of production? Recall that marginal cost is the change in cost divided by the change in quantity, or the change in cost when quantity increases by o

(d) What is the average fixed cost when q = 100 (in thousands)? What is the average fixed cost as a function of q?

(e) Suppose the company borrows money and automates its factory. Its fixed cost rises by $50 (thousand), but its variable cost as a function of q falls to $45q. What is the new average cost function? How much output does the firm need to produce in order for the automation to be profitable (in order for its average cost to be lower after the automation)?

Consider a firm with a production function given by q=187N, where q is the quantity produced and N is the number of workers hired. The firm sells its product in a competitive market, and the market price of its good is p=1.

The firm, however, is the only employer in the town where it operates, and hence it does not take the cost of labour as given. The inverse labour supply function in this town is given by w=45+0.04N2.

1.

a) Solve for the profit-maximizing choice of N.

b) What will the wage be in this town?

c) Is the wage equal to, greater than, or less than p MPN (where p is the price of the good and MPN is the marginal product of labour)? Explain intuitively why this is the case in this setting.

d)If the government were to intervene in this market by setting a minimum wage, what would be the optimal level at which to set the minimum wage, if the government's objective is to increase employment as much as possible?

4. Suppose that a firm's inputs are labor (variable costs) and trucks (fixed costs) and the firm owns one truck and the cost function, in the short run, is C(q) = 50 + q + 1 2 q 2 .

(a) The marginal cost function is now MC(q) = 1 + q. Marginal cost is equal to the derivative of the cost function or C/q for very small q. The derivative of q is 1 and the derivative of 1 2 q 2 is q. What are the average total cost and the average variable cost functions? Note: I'm asking for functions of q, or AC(q) and AV C(q).

(b) Graph the three cost functions, MC(q), AC(q), and AV C(q). Recall that to graph a function, you pick 3 or 4 different value of q (on the horizontal axis) and find the value of the cost per unit (the vertical axis), then you plot the points, and then you connect them to draw the function.

(c) If the price is $15, how much output will the firm produce if it is maximizing profits? Assume the firm is a price-taker and its output decision does not impact the price.

(d) Suppose that in the long run the firm can purchase more trucks (and of course also hire more labor). If the firm expects the price to stay at $15, will the firm buy more trucks? Answer intuitively. The question is, is this business profitable so that if it doubled its labor and doubled its capital (trucks) it would make more money? Equivalently, you might ask would another firm want to enter this industry if it had the same costs as you? Hint: think about what quantity the firm produces and what is the firm's average costs when it produces this quantity. Extra: If you want to answer this mathematically, note that with two trucks the fixed costs rise to 100 and the average variable cost function becomes q + 1 4 q 2 .

(e) If the firm expects the price to drop to $9 and stay at $9, will the firm buy more trucks? Explain. Again, answer intuitively. Is its business profitable so that if it doubled its labor and doubled its capital (trucks) it would make more money? Hint: think about what quantity the firm produces and what the firm's average cost is when the firm produces this quantity.

Consider the following transactions: 1. Top Bank repays a $40m interbank loan from Bottom Bank. 2. Middle Bank pays a $1m fine to the RBA, the Australian central bank, for not meeting reserve requirement. 3. Bottom Bank pays $0.5m interest on its RBA lending facility loan. 4. Top Bank pays $20m on the government's account at the RBA for the purchase of government bonds newly issued. 5. The RBA pays $3m salaries to its employees, who have a bank account at Middle Bank.

a. (i) Show how the balance sheet of the RBA is affected by these transactions. Represent all transactions in the same balance sheet and indicate for each transaction the item number as shown in the list.

a. (ii) Calculate the overall net impact of these transactions on the supply of Exchange Settlement Funds (ESF) in the banking system.

b. (i) Show in a detailed and well labelled diagram of market for reserves the effect on the equilibrium cash rate of the change in ESF described in a (ii) , combined with a decrease in the demand for reserves by $5m. Assume the market for reserves was originally at equilibrium at the current cash rate target of 0.10%.

b. (ii) Explain in words the mechanisms that led the adjusment from the original equilibrium to the new equilibrium.

c. (i) Using a different colour, represent the action of the RBA on the diagram in b(i) as part of its cash rate targeting policy at 0.10%.

c. (ii) Describe with details the transactions that the RBA is likely to have done to reach the outcome described in c (i).