4. Company P is a producer with constant marginal cost c. It gives a franchise contract...

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4. Company P is a producer with constant marginal cost c. It gives a franchise contract to a retailer in every region. Demand in a particular region is given by q = D-p, where p is the price and D can take values in (DH, DL) with DH > DL 0. Company P offers Retailer R the franchise contract T(q) = a +bq. This means that R has to pay P the sum T(q) if R sells q units in the region. (a) If the value of D is common knowledge, what is the optimal franchise contract for P? (R decides the amount q to sell.) (b) Now suppose that P knows the value of D when the contract is signed, but R gets to know the value of D after the contract is signed but before it chooses q. Derive the equilibrium contract [(a, b), (a, b)]. Explain the nature of this contract vis--vis the complete information con- tract. 4. Company P is a producer with constant marginal cost c. It gives a franchise contract to a retailer in every region. Demand in a particular region is given by q = D-p, where p is the price and D can take values in (DH, DL) with DH > DL 0. Company P offers Retailer R the franchise contract T(q) = a +bq. This means that R has to pay P the sum T(q) if R sells q units in the region. (a) If the value of D is common knowledge, what is the optimal franchise contract for P? (R decides the amount q to sell.) (b) Now suppose that P knows the value of D when the contract is signed, but R gets to know the value of D after the contract is signed but before it chooses q. Derive the equilibrium contract [(a, b), (a, b)]. Explain the nature of this contract vis--vis the complete information con- tract.