Alchem (L) is the price leader in the polyglue market. All 10 other manufacturers (follower [F] firms) sell polyglue at the same price as Alchem. Alchem allows the other firms to sell as much as they wish at the established price and supplies the remainder of the demand itself. Total demand for polyglue is given by the following function (QT=QL+QFQT=QL+QF): P=10,000−4QTP=10,000−4QT   Alchem’s marginal cost function for manufacturing and selling polyglue is MCL=5,000+6QLMCL=5,000+6QL and the aggregate marginal cost function for the other manufacturers of polyglue is ΣMCF=2,000+4QFΣMCF=2,000+4QF. To maximize profits, Alchem should produce     units and charge a price of     per unit.   What is the total market demand for polyglue at the price established by Alchem?    units.   How much of total demand do the follower firms supply?    units.

Imagine that the cell-phone market is made up of one large firm that leads the industry and sets its own price first, while smaller firms in the industry follow. There are 20 such smaller firms, each with a supply function of q; = 67.50 + for i = 1,2, ..., 20 firms, while pis the per-unit price. Total market demand for cell phones is given by the function Q = 6, 700.00 – p. If the cost function for the leading firm is CL(qL) = 109L, calculate the following values: %3D Leading firm's production: q1 = (Round to two decimals if necessary.) Total follower firm production: qF = (Round to two decimals if necessary.) Equilibrium price: p = $ (Round to two decimals if necessary.)

Parkleigh Pharmacy is an upscale department store in Rochester, NY, that sells personal accessories and home decorations. Kaufmann’s is a departmental store based in Pennsylvania and has several stores in Rochester, NY. Kaufmann carries a broad range of products and caters to middle-class customers. A salesperson at Parkleigh is paid a straight hourly wage (e.g., no sales commission) and 30% discount from purchasing any product from Parkleigh’s store. A salesperson at Kaufmann gets an hourly wage lower than Parkleigh’s hourly wage but gets 5% commission on sales. However, the product salesperson buys from Kaufmann without a discount. Explain why does Kaufmann pays sales commission, and Parkleigh doesn’t

A new restaurant – Uovo – has just opened in West L.A. It is serving the upscale market, with truly outstanding pasta that is flown in overnight from Bologna, Italy. Uovo offers a fixed-price menu with appetizer, three dishes of pasta, and a delicious tiramisu for dessert. The restaurant faces the following demand function: Q = 600 - 4P where Q is the number of guests per day. The marginal cost is constant at $50 per customer (including expenses for ingredients and personnel). The restaurant is paying a rent of $2,000 per day. What is the profit-maximizing number of guests that Uovo should serve each day, and what price should Uovo charge to maximize profit? What is the elasticity of demand at the optimal price and quantity? Is demand elastic or inelastic at this point? From what we learned in class, does it make sense for the restaurant to operate in this area of the demand curve (elastic/inelastic part)? What is the profit of the restaurant at the optimal price and quantity, and what…