In April 2025
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QUESTION 1:
A firm faces the demand schedule p = 200 - 2Q and the total cost function
TC = 2/3 Q^3 - 14Q^2 + 222Q + 50
Derive expressions for the following functions and find out whether they have maximum or minimum points. If they do, say what value of q this occurs at and calculate the actual value of the function at this output.
Marginal cost.
Average variable cost
Average fixed cost
Total revenue
Marginal revenue
Profit
Construct your own example of a function that has a turning point. Check the second-order conditions to confirm whether this turning point is a maximum or a minimum.
Explain why a firm which is a monopoly seller in a market with the demand schedule P = 66.8 - 0.4Q and which faces the total cost schedule TC = 220 + 120Q - 12Q^2 + 0.5Q can never make a positive profit.
Suppose the supply curve for good X passes through the point P 5 $25, Qs 5 500. Give two interpretations of this point on the supply curve.
Find GNP gap point if the natural rate of unemployment is 9% and actual rate of unemployment is 5%.
Qd = 100 – 5P and Qs = –20 + 3P. If the price is R10, then there will be a shortage of
Some restaurants have shortened their hours of operations (opening later and/or closing earlier) rather than shut down completely. Why might that be a good idea? Explain your reasoning using the relevant economic concepts.
Suppose tha a consumer’s utility function is U(x,y)= . The price of x goods Px and the price of y goods is Py with both prices positive. The consumer has income M.
(1) Draw the indifference curve and the budget line.
(2) How much x goods and y goods does this consumer pick out to maximize his utility(It is called the consumer equilibrium point) when M=100, Px=10 and Py=5
(3) Derive the individual demand curve.
(4) Is the relation between the two goods, x and y, substitute goods or complimentary goods or independent goods?
(5) Calculate the price elasticity of each goods, the income elasticity of each goods and cross elasticity between two goods?
(6) Based on this indifference curve and budget line, Explain the substitution effect and the income effect when the price of x goods increases.
The demand and supply function of a good are given by
P = -3Qd +100
P =2Qs +50
Where p, Qd and Qs denotes the price, quantity demanded and quantity supplied respectively.
Calculate the equilibrium price and quantity.
Explain why a monopoly may not always have a higher price and lower output than perfect competition?
A highly competitive market is made up of 100 identical firms. Each firm has a short-run
marginal cost function as follows:
MC = 10 + Q,
where Q represents units of output per unit of time. The firm's average variable cost curve
intersects the marginal cost at a vertical distance of 10 above the horizontal axis.
a. Determine the market short-run supply curve.
b. Calculate the price that would make 2,000 units forthcoming per time period.
How do think the development of other copying machines affected the elasticity of demand for Xerox machines?
