3) AD SPENDING: GET YOUR NAME OUT THERE! Artists know (or learn) that toiling away in obscurity isn't usually profitable; it is better to invest some resources in self- promotion and building a fanbase. We can model this with an advertising investment shifting out the demand curve. But if advertising is costly, then more advertising brings both added benefits and costs. Given this tradeoff, how much should one spend? Suppose an artistic monopolist (e.g., the maker of a board game) chooses both output and advertising to maximize its profit. It faces the market inverse demand function P[Q,A] = 100 + √A - Q, where P is price, Q is output, and A is the level of advertising. The firm's constant marginal cost of production (based on Q is 10 and its constant cost per unit of advertising (based on A) is 1. TIPS: Think of the P[Q] = 100-Q demand curve, but then shift it out by √A to account for advertising. Total cost will have two parts: the factory cost (which depends on Q) and the advertising cost (which depends on A). a) Explain to a layperson the intuitive meaning of the functional form √A by comparing it to A or A². b) Suppose the firm has signed a market contract and committed to advertising spending of A=400 in the short run, so it only can choose output Q. Find the firm's short-run profit maximizing results (Q**,Ā = 400, P**). c) Suppose instead that the firm can choose ad spending. Find the firm's profit-maximizing results, (Q*,A*, P*). TIP: Find the two first-order conditions (37, and 87) and combine them. TIP: Imagine climbing a three-dimensional mountain, where A the altitude (height) is a function of map coordinates. The peak of this smooth/rounded mountain should occur where the slopes in the North-South and the East-West dimensions are simultaneously zero (because if not, then there is a way of ascending in one direction!). Here, height is profit, the North-South coordinate is Q, and the East-West coordinate is A, so T* occurs at (Q*, A*). d) A famous result from the advertising literature is the Dorfman-Steiner condition, which says that the amount of one's total revenue (R) that should be spent on advertising (A) depends on both advertising elasticity of demand (AED) and price elasticity of demand (PED). Specifically, Using the A*, P*, and Q* you found in part (c), check if this holds. A AED = . R PED