Suppose a firm producing wood burning stoves has the following production functionQ(K, L) = 4K¹/2 [1/2Where L, the labour, and K, the capital are the 2 inputs of production and Q the quantityof stoves. Assume the price of one unit of L is £1 and the price of one unit of K is £2.a)b)Assume that K=9 in the short run. Draw the production function and calculate themarginal products of L as L changes from L= 1 to L= 6.What does an isoquant curve show? Draw the graph of a production isoquantrepresenting input combinations that will produce 8 units of output. c)d)e)h)Define the marginal rate of technical substitution. How would you represent it inthe previous graph?Does this production function exhibit increasing, decreasing or constant returns toscale?Suppose that the market for wood burning stoves is also perfectly competitive. Firms in themarket are identical and each firm has a total cost function: TC(q) = 3q³ − 9q² + 15q + 20.q is given in number of stoves and P in hundreds of pounds.f)If the equilibrium price in the wood burning stoves is equal to £15, what is thequantity of stoves supplied by a firm?What is the profit made by a firm?Find the equation for the average variable cost of a firm. Calculate the shutdownprice of a firm. What does it represent?Comment about the situation of the firm based on your answer in g) and h).Given your answer in g), comment on what is likely to happen on the market in thelong-run. Illustrate your answer with graphs.i)j)Suppose the firm is producing Q = 48 stoves using 9 units of labour and 16 ofcapital. Is the firm producing its current level of output at the minimum cost? Ifnot, what should the firm do?

Production function is the mathematical expression of the amount of output a system or firm produces…

Suppose a firm producing wood burning stoves has the following production function Q(K, L) = 4K ¹/21/2 Where L, the labour, and K, the capital are the 2 inputs of production and Q the quantity of stoves. Assume the price of one unit of L is £1 and the price of one unit of K is £2. a) b) Assume that K=9 in the short run. Draw the production function and calculate the marginal products of L as L changes from L= 1 to L= 6. What does an isoquant curve show? Draw the graph of a production isoquant representing input combinations that will produce 8 units of output.

Suppose a firm producing wood burning stoves has the following production function Q(K, L) = 4K ¹/21/2 Where L, the labour, and K, the capital are the 2 inputs of production and Q the quantity of stoves. Assume the price of one unit of L is £1 and the price of one unit of K is £2. a) b) Assume that K=9 in the short run. Draw the production function and calculate the marginal products of L as L changes from L= 1 to L= 6. What does an isoquant curve show? Draw the graph of a production isoquant representing input combinations that will produce 8 units of output.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

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Concept explainers

Isocost and Isoprofit Curve Analysis

An isocost curve in the production theory that is a crucial part of economics depicts different combinations of factor inputs at a given market cost. In other words, this shows all the combinations of production factors that cost the same for the firm to employ. Usually, this can be depicted as a downward sloping straight line when the firms act as the price-takers in the factor markets. The slope of this mainly depicts the relative prices of different production factors.

Question

Suppose a firm producing wood burning stoves has the following production function
Q(K, L) = 4K¹/2 [1/2
Where L, the labour, and K, the capital are the 2 inputs of production and Q the quantity
of stoves. Assume the price of one unit of L is £1 and the price of one unit of K is £2.
a)
b)
Assume that K=9 in the short run. Draw the production function and calculate the
marginal products of L as L changes from L= 1 to L= 6.
What does an isoquant curve show? Draw the graph of a production isoquant
representing input combinations that will produce 8 units of output.

c)
d)
e)
h)
Define the marginal rate of technical substitution. How would you represent it in
the previous graph?
Does this production function exhibit increasing, decreasing or constant returns to
scale?
Suppose that the market for wood burning stoves is also perfectly competitive. Firms in the
market are identical and each firm has a total cost function: TC(q) = 3q³ − 9q² + 15q + 20.
q is given in number of stoves and P in hundreds of pounds.
f)
If the equilibrium price in the wood burning stoves is equal to £15, what is the
quantity of stoves supplied by a firm?
What is the profit made by a firm?
Find the equation for the average variable cost of a firm. Calculate the shutdown
price of a firm. What does it represent?
Comment about the situation of the firm based on your answer in g) and h).
Given your answer in g), comment on what is likely to happen on the market in the
long-run. Illustrate your answer with graphs.
i)
j)
Suppose the firm is producing Q = 48 stoves using 9 units of labour and 16 of
capital. Is the firm producing its current level of output at the minimum cost? If
not, what should the firm do?

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Step 2: Illustration of production function

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Step 3: Understanding Isoquant

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Step 4: Understanding MRTS

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Step 5: Calculation of returns to scale

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Step 6: Calculating efficient allocation

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Step 7: Calculation of market equilibrium

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Step 8: Calculation of Profit

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