Hi, I just need to make sure i solved the problem correctly and my answers are correct. Thanks

WK4 Problem Solving Assignment: Duopoly Competition Suppose that currently, all of the handmade sweaters in Alaska are supplied by only two firms, Granny's Handknits and A Stitch in Time. The demand curve for sweaters in this market is given by P = 350 - Q, where P is market price and ( is quantity. The marginal cost (for knitter's labor and yarn) is constant and equal to $50 per sweater, and the fixed cost is $0. a. Assume that this market operates under the assumptions of the Cournot model. Derive the best response (reaction functions) of each firm, and use these to determine the number of sweaters provided by each firm, the market price, and each firm's profit in a Nash equilibrium. Granny's best response function: 300=2q1+q2 A Stitch's best response function: 300=q1 + 2q2 Granny's Output: q1=100 A Stitch's Output: 91=100 Market Price: P= $150 Granny's Profit: $10,000 A Stitch's Profit: $10,000 b. Suppose now that the two firms collude and form a cartel (ie. they act as if they merged and formed a monopolist called "Grannies in Time"). The costs of production are unchanged. Find the market price and quantity, and the new firm's profit. Grannies in Time's output: 150 Market Price: $200 Grannies in Time's profit: 522,500 c. Suppose instead that the two firms compete in such a way that their market power is totally vanished. That is, the combined production of the two firms is the same as an industry with many firms under perfect competition. Calculate the combined output and market price now. Combined Output: 200 Market Price: $350