Could someone help me out with these questions

6. (250 points; 25 minutes) Your company produces lawn mowers. Each lawn mower needs one engine. You produce your own engines. The market for lawn mowers is competitive and the market price is $1,100. Given the engine, there are additional costs of $900 to assemble the lawn mower. (a) Your firm has one fabrication plant for engines. Its marginal cost is MC = 10Q. There are no fixed costs. All quantities are expressed in thousands of engines or lawn mowers. What is the optimal production levels Q for your engine fabrication plant? What is the optimal transfer price for an engine? (b) Your firm has two fabrication plants for engines; their marginal cost structures are given as MC1 = 10 Q1 MC2 = 10+ 10 Q2 There are no fixed costs. All quantities are expressed in thousands of engines or lawn mowers. What are the optimal production levels Q and Q2 for your two engine fabrication plants? What is the optimal transfer price for an engine? (c) Take the situation of part b) but suppose that there is also a competitive outside market for engines, where engines can be purchased or sold for $ 250. What are the optimal production levels Q and Q2 for your two engine fabrication plants, how many lawn mowers Q should you produce, and how many engines should be bought or sold in the outside market? What is the optimal transfer price? 7. (300 points, 30 minutes) [The following is based on actual events, though details are fictionalized for simplicity./ In the early 1990s activist groups supported by Ralph Nader filed a recall petition against 10 million General Motors trucks, claiming that their fuel tanks could explode in a crash. In 1993, General Motors proposed to settle the resulting lawsuits by giving coupons to all 10 million affected owners. Each coupon allows one to receive $1000 off any new GM truck purchased in 1994. (The coupons expire at the end of 1994.) These coupons are fully transferable: if someone with a coupon gives / sells it to someone else, that person can also use it to get $1000 off a new GM truck. If the proposal goes ahead, all parties expect a competitive market to arise in which these coupons will be actively traded. GM has zero fixed costs and marginal cost of $10,000 per truck. Demand for GM trucks in 1994 is given by D(p) = 8,000,000 - 200p (a) Suppose that the judge does not allow the settlement. In this case, what price will GM charge for its trucks? What is GM's profit and what is consumer surplus? (b) Suppose now that the judge allows the settlement and that GM charges a price of $26,000 for trucks. Construct the resulting demand and supply curves in the market for coupons. What is the price at which coupons will trade? Given this price for the coupons, how many trucks will GM sell? What is GM's profit and what is consumer surplus? How much did GM's profit and consumer surplus change, relative to your answer in (a)?