ECO200Y1 Lecture Notes - Lecture 14: Production Function, Demand Curve, Isocost
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ECONOMICS 200
Lecture Assignment #14
Theory of the Firm: Inputs, Output, Costs
Source: BB, Chapter 7(skip the Appendix) and Chapter 8 (skim 8.3 and 8.4 for your
interest, not for test marks and skip the Appendix) . (Some parts will be dealt with in
LA#15; see comment in the paragraph below).
The previous assignment dealt with production relationships i.e., the relationship between
inputs and outputs. This assignment deals with the relationship between outputs and
costs (and the costs, of course, are related to the expenditures on the inputs necessary to
make the output).
Once again, assume a single output, and only two inputs (K and L) with fixed input prices
(PKand PL), measured at opportunity cost. (The implications of the last statement
“measured at opportunity cost” will be analyzed in LA#15.)
1. Isocost Line
1.1 Define, and plot a typical isocost line (TC = PK*K + PL*L) where TC is a given
value.
1.2 What is its slope?
1.3 What happens to the isococt line when:
a) The price of K changes
b) The price (wage rate) of L changes
c) The input budget (value of TC) changes.
2. Optimum Production Point
Assume that the firm wishes to maximize profits. Consider the response of the firm to
the following optimum objectives, using an isoquant-isocost diagram with convex
isoquants, and assuming an interior solution:
2.1 Output maximization, for a given level of total cost (i.e., a given input budget)
2.2 Cost minimization, for a given level of output
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2.3 Here is a simple problem with an interior solution. The Production Function is q
= K1/2 * L1/2. Input prices are PK= $4 and PL= $1.
a) What is the maximum q that can be produced, with an input budget of $160?
b) To produce that optimum output, how much K and L will be utilized?
c) What is the lowest total cost possible to produce 40 units of output?
d) To produce that level of output at the lowest cost, how much K and L will be
utilized?
2.4 Needless to say, there are “non-standard” situations such as:
•Convex isoquants with a corner solution
•Fixed proportion Production Function and L-shaped isoquants
•Linear Production Function with linear isoquants.
Having mastered Consumer Theory with identical “non-standard” Utility
Functions, you know how to solve these!
2.5 Consider a firm that is in equilibrium (i.e., at a production point whereby the
MRTS = input price ratio). What are the implications for the firm if the price of
labour rises? [Assume interior solutions.]
2.6 Consider ABC Company that has a production budget of $160 and faces fixed
input prices for K and L of $4 and $1 respectively. According to the answer to
2.3 above, it knows that the optimum output is X units (you solved for X). Now
suppose that the wage rate rises to $4.
a) What happens to the maximum amount of output that can be produced?
b) What happens to the K/L ratio of inputs utilized?
c) Alternatively, what would it cost now to produce the original level of output
(i.e., the X units you calculated in 2.3 above)?
Calculate the values for the questions above and demonstrate on a diagram too.
[The diagram involves convex isoquants and interior equilibrium points, as evidenced by your
calculations.]
2.7 Consider the production function we have been using in this question, namely q =
K1/2 * L1/2. For a given quantity of output:
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ECO200Y1 Full Course Notes
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Document Summary
Source: bb, chapter 7(skip the appendix) and chapter 8 (skim 8. 3 and 8. 4 for your interest, not for test marks and skip the appendix) . (some parts will be dealt with in. The previous assignment dealt with production relationships i. e. , the relationship between inputs and outputs. This assignment deals with the relationship between outputs and costs (and the costs, of course, are related to the expenditures on the inputs necessary to make the output). Once again, assume a single output, and only two inputs (k and l) with fixed input prices (pk and pl), measured at opportunity cost. (the implications of the last statement. Measured at opportunity cost will be analyzed in la#15. ) Define, and plot a typical isocost line (tc = pk*k + pl*l) where tc is a given value. 1. 3 what happens to the isococt line when: the price of k changes, the price (wage rate) of l changes, the input budget (value of tc) changes.
