11) Sam has been spending a lot of time with Jamie since their yoga class. Inspired to live a new lifestyle, Jamie has also gotten seriously into gardening. Suppose Jamie's production function and marginal products for producing backyard lettuce are given by: Y(M,L)=M1/2L1/2 3 MPM=2M1/2L1/2MPL=2L1/2M1/2 Y is the quantity of lettuce produced, L is the number of hours Pat works the garden, and M is the amount of an indexed unit of all other factors. M would include raw materials (seeds, dirt, fertilizer etc.), capital (hose, chicken wire etc.), and land (backyard space) used in production. Jamie uses 100 hours of their time and 4 units of M in their lettuce garden, making 20 heads of lettuce at the end of summer. Each unit of M cost $5 and the price of lettuce at the grocery store is $5 per head. Jamie brags "I saved $80 growing my own lettuce!". a) Do you agree with your Jamie - did they save $80 on lettuce? Why or why not. b) Suppose Jamie works a job with flexible hours at the local hemp store that pays $20 an hour. If they valued all inputs in the production function at their opportunity cost, what is their economic profit from growing lettuce? c) Does this value necessarily imply that growing backyard lettuce is a bad use of these inputs? d) Having taken Econ 301, Sam decides to advise Jamie on how to minimize their costs of lettuce production. What functions might Sam derive to determine Jamie's cost minimizing combination of inputs? e) Derive these functions. Given the input prices above, calculate the optimal amount of M and L to produce Y=20. f) Suppose the Jamie was so impressed by the economic cost savings from this exercise and planned to start a business selling backyard lettuce. Given the input and product prices above, would Sam invest in this business? 11) Sam has been spending a lot of time with Jamie since their yoga class. Inspired to live a new lifestyle, Jamie has also gotten seriously into gardening. Suppose Jamie's production function and marginal products for producing backyard lettuce are given by: Y(M,L)=M1/2L1/2 3 MPM=2M1/2L1/2MPL=2L1/2M1/2 Y is the quantity of lettuce produced, L is the number of hours Pat works the garden, and M is the amount of an indexed unit of all other factors. M would include raw materials (seeds, dirt, fertilizer etc.), capital (hose, chicken wire etc.), and land (backyard space) used in production. Jamie uses 100 hours of their time and 4 units of M in their lettuce garden, making 20 heads of lettuce at the end of summer. Each unit of M cost $5 and the price of lettuce at the grocery store is $5 per head. Jamie brags "I saved $80 growing my own lettuce!". a) Do you agree with your Jamie - did they save $80 on lettuce? Why or why not. b) Suppose Jamie works a job with flexible hours at the local hemp store that pays $20 an hour. If they valued all inputs in the production function at their opportunity cost, what is their economic profit from growing lettuce? c) Does this value necessarily imply that growing backyard lettuce is a bad use of these inputs? d) Having taken Econ 301, Sam decides to advise Jamie on how to minimize their costs of lettuce production. What functions might Sam derive to determine Jamie's cost minimizing combination of inputs? e) Derive these functions. Given the input prices above, calculate the optimal amount of M and L to produce Y=20. f) Suppose the Jamie was so impressed by the economic cost savings from this exercise and planned to start a business selling backyard lettuce. Given the input and product prices above, would Sam invest in this business