Question

In: Economics

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

  1. Kent sells lemonade in a competitive market on a busy street corner. His production function is F(L, K) = L1/3 K1/3 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.

Solutions

Expert Solution


Related Solutions

Earnie sells lemonade at a busy street corner in Rollaville. His production function is f(x,y) =...
Earnie sells lemonade at a busy street corner in Rollaville. His production function is f(x,y) = x^1/4*y^1/2 where output is measured in gallons, x is the number of pounds of lemons he uses, and y is the number of labor-hours spent squeezing them. The price of a pound of lemons is $1 and the wage rate for the lemon-squeezer (Earnie’s best friend, Bert) is also $1. While Earnie can hire Bert for any amount of time, he has only three...
Kelly sells orange juice in a competitive market on a busy street corner in New York....
Kelly sells orange juice in a competitive market on a busy street corner in New York. Her production function is ?(?1, ?2) = ?1 1/3 ?2 1/3, where output is measured in gallons, ?1 is number of pounds of oranges she uses, and ?2 is the number of labor-hours spent squeezing them. ?1 = $16 is the cost of a pound of oranges and ?2 = $2 is the wage rate for orange-squeezers. At the cost minimizing input bundle, how...
Beth is a second-grader who sells lemonade on a street corner in your neighborhood. Each cup...
Beth is a second-grader who sells lemonade on a street corner in your neighborhood. Each cup of lemonade costs Beth $0.20 to produce; she has no fixed costs. The reservation prices for the 10 people who walk by Beth's lemonade stand each day are listed in the following table. Person 1 2 3 4 5 6 7 8 9 10 Reservation price $0.50 $0.45 $0.40 $0.35 $0.30 $0.25 $0.20 $0.15 $0.10 $0.05 Beth knows the distribution of reservation prices (that...
Beth is a second-grader who sells lemonade on a street corner in your neighborhood. Each cup...
Beth is a second-grader who sells lemonade on a street corner in your neighborhood. Each cup of lemonade costs Beth $0.90 to produce; she has no fixed costs. The reservation prices for the 10 people who walk by Beth's lemonade stand each day are listed in the following table.   Person 1 2 3 4 5 6 7 8 9 10 Reservation price $1.50 $1.40 $1.30 $1.20 $1.10 $1.00 $0.90 $0.80 $0.70 $0.60 Beth knows the distribution of reservation prices (that...
Cost of Competitive Firm In Stockholm, there is a competitive market for the production of canopy...
Cost of Competitive Firm In Stockholm, there is a competitive market for the production of canopy beds. Max’s canopy bed production firm can make at most six canopy bed’s per week. Quantity Fixed Cost ($) Variable Cost ($) Total Cost ($) Marginal Cost ($) 0 0 5000 --- 1 5000 2000 2 6000 3 6000 4 8000 5 35000 6 42000 Complete the four cost columns in the table above. If the market price of pianos is $6000 this week,...
Cost of Competitive Firm In Vienna, there is a competitive market for the production of upright...
Cost of Competitive Firm In Vienna, there is a competitive market for the production of upright pianos. David’s piano production firm can make at most six pianos per week. Quantity Fixed Cost ($) Variable Cost ($) Total Cost ($) Marginal Cost ($) 0 2000 --- 1 5000 2 2000 11000 3 18000 4 8000 5 37000 6 45000 Complete the four cost columns in the table above. If the market price of pianos is $8000 this week, how many pianos...
Suppose Andy sells basketballs in the perfectly competitive basketball market. His output per day and costs...
Suppose Andy sells basketballs in the perfectly competitive basketball market. His output per day and costs are as follows: Output per Day (Q) Total Cost (TC) 0 $10.00 1 $20.50 2 $24.50 3 $28.50 4 $34.00 5 $43.00 6 $55.50 7 $72.00 8 $93.00 9 $119.00 1) Make a table with Quantity (Q), Total Cost (TC), Fixed Cost (FC), Variable Cost (VC), Average Total Cost (ATC), Average Variable Cost (AVC), Marginal Cost (MC), and Marginal Revenue (MR) on it (using...
The table below represents a production schedule for Quincy’s Quiche Corner, a restaurant in a mall that sells quiches.
The table below represents a production schedule for Quincy’s Quiche Corner, a restaurant in a mall that sells quiches. Assume Quincy’s operates in a perfectly competitive environment (in both input and output markets), so it is both a price-taker and a wage-taker.a) Fill in the missing values in the table, assuming the selling price per quiche is $3.WorkersOutput (quiches)Marginal Product Value of Marginal Product                           0                 0     1                 10                        10                      $30     2                 18                        _____                            $24     3                 24                            6                      _____    ...
Problem. Suppose that, in a large city, 200 identical street vendors compete in a competitive market...
Problem. Suppose that, in a large city, 200 identical street vendors compete in a competitive market for hot dogs. 1. The vendors total costs to produce q hot dogs is, C(q) = 1/4q + 1/8q². What is the marginal cost function of each firm? 2. Given your answer from above, how many hot dogs will each vendor produce if offered a price of $4 per hot dog? 3. Using your answer from part 1 of this problem, what is the...
A competitive firm has a production function ?(?, ?) = (? + ?)1/2 where ? and...
A competitive firm has a production function ?(?, ?) = (? + ?)1/2 where ? and ? stand for inputs capital and labour respectively. The price of capital is ?, and the price of labour is ?. Which of the following is true? Regardless of ? and ?, cost minimisation requires that ? = ?. If ? > ?, contingent demand for labour is 0. The technology has increasing returns to scale. If ? < ?, profit maximisation requires that...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT