Producer’s surplus is related to the concept of consumer’s surplus, but it represents the net benefit to a supplier of producing a commodity at a certain price.

Producer’s surplus is related to the concept of consumer’s surplus, but it represents the net benefit to a supplier of producing a commodity at a certain price. Producer’s surplus can be measured as the area above the supply curve but below the market price.

(a) Given the linear supply curve q = 10p + 50, assume that the initial price equals 1 and the quantity supplied equals 60. Use integration to determine the change in producer’s surplus when the price rises to 2. Does this represent an increase or decrease in producer’s surplus?

(b) Producer’s surplus might also be considered as the benefit accruing to a sup- plier of a factor of production in excess of what is required. In the case of labor, producer’s surplus can be measured as the area above the supply curve and below the wage rate. Consider Sally, who is willing to supply her labor according to the function q = 15Vp. Use integration to evaluate the change in producer’s surplus when the wage rate rises from $2 per hour to $4 per hour.

7. Capital formation is the process of adding to a given stock of capital. In a continu- ous-time model, capital stock can be expressed as a function of time, K(t). Investment, (t), represents the rate of capital formation and can be expressed as the derivative of capital stock with respect to time,

 dK(1) dt

Suppose that the investment varies with time in the following fashion:I(t) = 1-1/2 At time t = 9, the capital stock is 100. What is the capital stock at the end of period 25?