**Suppose that in a given production process a blueprint ( B) can be produced using either an hour of computer time (C) or 4 hours of a manual draftsman’s time (D). (You may assume C and D are perfect substitutes. Thus, for example, the firm could also produce a blueprint using 0.5 hour of C and 2 hours of D.)**

**a) Write down the production function corresponding to this process (i.e., express***B*as a function of*C*and*D*).**b) Suppose the price of computer time (***p*) is 10 and the wage rate for a manual draftsman (_{c}*p*) is 5. The firm has to produce 15 blueprints. What are the cost minimizing choices of_{D}*C*and*D*? On a graph with*C*on the horizontal axis and*D*on the vertical axis, illustrate your answer showing the 15-blueprint isoquant and isocost lines.

- a) Computers are four times as productive as draftsmen; an alternative way of saying this is that
*MP*= 4_{C}*MP*. Since_{D}*C*and*D*are perfect substitutes, we know the production function has the form*B = aC + bD*, where*a*and*b*are positive constants. Thus we can write the production function as*B = C +*(1/4)*D*. Note that this is consistent with generating one blueprint (*B =*1) from the following combinations of inputs: (*C, D*) = (1, 0), (*C, D*) = (0, 4), and (*C, D*) = (0.5, 2).

- b) Notice that . That is, the marginal product per dollar spent on computer time is always higher than the marginal product per dollar spent on draftsman time. So the optimal input combination involves
*D =*0 and*C =*The graph below illustrates the (dotted) isocost lines with slope = –*p*= –2, along with the (solid)_{C}/ p_{D}*B =*15 isoquant with slope = –*MP*–4._{C}/ MP_{D}=