Question

Suppose that the profit of a car producing firm is given by: ? = ?? − ?(?) And that the cost function is given by: ?(?) = 4? where ? is profits, ? is the price and ? is quantity produced. By setting profits equal to a constant level, ?, derive an expression for the isoprofit curve of this firm which expresses ? as a function of ? (for a given level of profits, ?).

c) Let the demand curve facing this firm be: ?(?) = 100 − 3? Find the profit maximising output and price for this firm and draw a diagram to illustrate the optimum (the diagram does not need to be accurate).

d) This optimum can be characterised by the condition, MRS=MRT (marginal rate of substitution equals marginal rate of transformation). Explain intuitively why it is optimal to have MRS=MRT in this context.

e) Explain what is meant by economies and diseconomies of scale and explain whether you think the cost function given in part (b) seems realistic for a car firm. How would the isocost function change if the average cost function exhibited both economies and diseconomies of scale?

Answer 1

e) Economies of scale are when the cost per unit of production (Average cost) decreases because the output increases. Diseconomies of scale are when the cost per unit of production (Average cost) increases because the output increases.

The average cost is given by Total Cost / Q = 4 . So it is constant here . But in a car firm we usually find economies of scale . As production increases efficiency or specialization increases which causes average cost to decline .

From the equation of isoprofit curve we can see that it depends on average cost . As the average cost falls , profit increases so firm can move to higher isoprofit curve . Opposite is the case for diseconomies of scale .