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A consumer must divide $600 between the consumption of product X and product Y

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A consumer must divide $600 between the consumption of product X and product Y. The relevant market prices are Px $10 and Py $40. a. Write the equation for the consumer's budget line. b. Illustrate the consumer's opportunity set in a carefully labeled diagram. c. Show how the consumer's opportunity set changes when the price of good X increases to $20. How does this change alter the market rate of substitution between goods X and Y? Q#2) A multiproduct firm's cost function was recently estimated as C(Q1, Q2) = 90 -0.5QjQ2 +0.4Q,2 +0.3Q22 a. Are there economies of scope in producing 10 units of product 1 and 10 units of product 2? b. Are there cost complementarities in producing products 1 and 2? Q#3) A firm produces output according to a production function F(KL) min [4K,8L). a. How much output is produced when K2 and L 3? b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing input mix for producing 8 units of output?