Figure 3.2 holds costs fixed at c = 4 and shows the effect of introducing discounting (moving from = 1 to = 0.77).

Figure 3.2 holds costs fixed at c = 4 and shows the effect of introducing discounting (moving from ρ = 1 to ρ = 0.77). This exercise asks you to create a figure showing the effect of changing costs, for a fixed discount factor.

(a) Using the the inverse demand function p = 20 − y, the initial stock x = 10, zero costs, c = 0, and the discount factor ρ = 0.77, create a figure showing the graphs of 20−y and ρ (20 − (10 − y)); make these graphs solid lines, for ease of identification. Identify the equilibrium period-0 sales as point B.

(b) Now graph the relevant lines (needed to identify the equilibrium) when c = 4; make these graphs dashed lines for ease of identification. Identify the equilibrium period 0 sales as point A.

(c) How does an increase in marginal costs from 0 to 4 affect period 0 sales? Provide a brief economic explanation for this result. 

20 Period 1 price minus cost feriod 0 price minus Cost 1s+ 10 Discounted period 1 price minus cost 10 11 12 Figure 3.2: Demand cost in period 0 (solid). Demand cost in period 1 (dashed). Present value of period 1 price - cost (dotted). For fixed costs, discounting increases period 0 sales.