Question

4, Uncertain Benefits. Consider the problem of supplying an input to a division of a firm or to a firm in a planned economy. Suppose the executive or planner knows the marginal cost function for the input, represented by the MC line in the figure However, the planner is uncertain about the marginal benefit. Her best estimate is the MB line. On that basis, the price should be p and the quanity q. Consider an error scenario in which the actual marginal benefit is higher, as represented by the MB' line. (a) Mark on the graph the quantity q' that would be produced using a price control p in the error scenario, and the quantity q" that would be efficient in the error 4 scenario (b) Identify the triangle that represents the loss in the error scenario with price control c) Identify the triangle that represents the loss in the error scenario with quantity (d) Discuss the relative sizes of the loss triangles and relate them to the slope of the p, and interpret it in terms of over- and under-production. control q. MC curve,

Answer 1

a) The Marginal Benefit curve slopes downwards while the Marginal Cost curve is increasing in quantity. Their intersection gives us the efficient equilibrium. In this diagram, q' is the quantity produced when price is controlled at p. However, the efficient quantity is q'' where the MB' curve intersects the MC curve.

null

b) Had there been no price control p, the market would have cleared at p' and produced q'' the efficient equilibrium quantity, Therefore, the shaded triangle shows underproduction.

c) With quantity control at q, the true marginal benefit curve MB' cuts the MC curve at A with a higher price p'. The shaded triangle shows the loss to the economy because of the error.

d) The relative size of the loss triangle increases as the MC curve becomes flatter or its slope decreases.