Hi, I need help with the following problem (see attached picture). Thanks!

1) Double marginalization and vertical mergers (30 points) Consider downstream and upstream rms which are both monopolies. Each unit of downstream output requires exactly one unit of an upstream product as an input and also incurs other marginal costs of 5 per unit. The upstream rm produces the input at a marginal cost of 5 per unit. Let the demand for the product sold by the downstream rm be given by Q(P) = 50 P where P is the downstream retail price. a) Suppose that the upstream rm sets a price w for the input to the downstream rm. Derive the prot maximizing price P for the downstream rm as a function of w. Use this function to obtain the derived demand for the upstream rm as a function of w. b) Use your answer to part a) to derive the prot function for the upstream rm as a function of w. Derive the prot-maximizing choice of w by the upstream rm. Calculate the choice of P given this prot-maximizing choice of w. Calculate the quantity sold by the downstream rm and the prots of the two rms. 0) Now assume that the two rms merge. Write their joint prot function as a function of the downstream price P. Calculate the post-merger prot-maximizing downstream price, the resulting output, and the prots of the merged rm. (1) What is the impact of this merger on total industry prots? What about on prices P charged to consumers