Total Cost function.
To find APL (Average Product of Labor), we need to divide the total product (Q) by the quantity of labor (L). APL = Q / L.
To find MPL (Marginal Product of Labor), we need to take the derivative of the production function with respect to labor (L) and evaluate it at a given quantity of labor (L). MPL = ∂Q / ∂L.
Using the given production function Q(L,K) = L^(3/4) * K^(1/4), and assuming capital (K) is fixed, we can ignore it for now.
1. APL = Q / L = (L^(3/4) * K^(1/4)) / L
Canceling out L,
APL = K^(1/4) * L^(-1/4)
2. MPL = ∂Q / ∂L = (3/4) * L^(-1/4) * K^(1/4)
Now, let's move on to the second question.
To find the minimum value of AVC (Average Variable Cost) and MC (Marginal Cost), we need to differentiate the Total Cost (TC) function with respect to quantity (Q) and equate it to zero.
Given TC = (1/3)Q^3 - 2Q^2 + 60Q + 100,
1. AVC = VC / Q, where VC is the Variable Cost.
As VC = TC - FC (Fixed Cost), and FC is not given, we cannot directly calculate AVC. We need more information to determine FC.
2. MC = ∂TC / ∂Q = Q^2 - 4Q + 60
Moving on to the third question,
Oligopoly and monopolistically competitive market structures have similarities and differences.
Similarities:
- Both market structures are characterized by imperfect competition, meaning that there are some barriers to entry and firms have some degree of market power.
- In both structures, firms can differentiate their products and engage in non-price competition.
- Both structures can lead to a wide range of prices and outputs.
Differences:
- Oligopoly has a smaller number of firms compared to monopolistically competitive markets, where there are many firms.
- In oligopoly, there is a high degree of interdependence among firms, as their actions directly affect each other's profits. In monopolistic competition, firms are relatively independent.
- Oligopoly often experiences collusion or strategic behavior, with firms working together to maximize joint profits. Monopolistic competition does not usually involve collusion.
- Oligopolistic firms may engage in price leadership, where one firm sets the price and other firms follow. This is not observed in monopolistically competitive markets.
Finally, for the fourth question,
To find the profit-maximizing level of output for a firm operating in a perfectly competitive market, we need to equate marginal cost (MC) to the market price (P).
Given the market price P = 4 and the total cost function TC = (1/3)Q^3 - 5Q^2 + 20Q + 50,
1. MC = dTC / dQ = Q^2 - 10Q + 20
2. Set MC equal to the market price P:
Q^2 - 10Q + 20 = 4
Q^2 - 10Q + 16 = 0
Solving this quadratic equation will give us the profit-maximizing level of output for the firm.
9. Suppose the production function is given by Q(L,K) = L3/4K
1/4 Assuming capital is
fixed, find APL and MPL.
10. Given a short run cost function as TC = 1/3Q3
-2Q2
+60Q+100 , find the minimum
value of AVC and MC.
11. What are the similarities and differences between oligopoly and monopolistically
competitive market structure?
12. A firm operates in a perfectly competitive market. The market price of its product is
4 birr and the total cost function is given by TC= 1/3Q3
-5Q2
+20Q+50, where TC is the
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1 answer