Kent sells lemonade in a competitive market on a busy street corner. His production function is...

Kent sells lemonade in a competitive market on a busy street corner. His production function is F(L, K) = L^1/3 K^1/3 where output q is gallons of lemonade, K is the pounds of lemons he uses and L is the number of labour-hours spent squeezing them. The corresponding marginal products are MPL= 13L-23K13 and MPK= 13L13K-23. Every pound of lemons cost r and the wage rate of lemon squeezers is w.
1. Prove that this production process has decreasing returns to scale.
2. On a graph with hours of lemon-squeezing (L) on the horizontal axis and pounds of lemons (K) on the vertical axis, illustrate an isoquant that represents a particular production level q. What is the equation of the isoquant?
3. What is the equation for a slope of an isoquant? Is it constant? What does the slope indicate? Explain.
4. What are the conditions that identify the cost minimizing bundle for any output? Illustrate on a clearly labelled diagram.
5. Set up the cost minimization problem and solve for the conditional input demands as functions of the exogenous variables.
6. Derive the cost function (as a function of only the exogenous variables).
7. Continue with total cost function derived in previous part and derive the average cost. Is it upward or downward sloping? Explain.

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Expert Solution

Rahul Sunny answered 1 month ago

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