Question 2 answers:
A.Suppose the supply function for product X is given by Qxs = −30 + 2Px − 4Pz.
When Px= $600 and Pz=$60, the amount of product X produced is:
Qxs = -30 + 2($600) – 4($60)
Qxs = 930 units.
Therefore, when Px is $600 and Pz is $60, the amount of product X produced is 930 units.
- when Px = $80 and Pz = $60, we need to substitute these values in the supply function and solve for Qxs:
Qxs = −30 + 2Px − 4Pz
Qxs = −30 + 2($80) − 4($60)
Qxs = −110
Therefore, when Px = $80 and Pz = $60, the amount of product X produced is −110.
- When Pz = $60. For good X, the supply function and inverse supply function should be determined. Qxs = −30 + 2Px − 4Pz
Qxs + 30 + 4Pz = 2Px
Px = (Qxs + 30 + 4Pz) / 2
Therefore, the supply function for product X when Pz = $60 is:
Px = (Qxs + 150) / 2
So, Qxs = 2Px − 150
The graph of the inverse supply function is shown below:
75 150
Question 3
We may use the elasticity values and the following formulas to calculate how much the consumption of good X will vary as a result of these changes:
- The cost of item X drops by 6%:
The demand for X has an own price elasticity of -5, which indicates that a 1% drop in X's price results in a 5% rise in X's quantity demanded. As a result, a 6% drop in X's price would result in a 30% rise in X's quantity required.
- The cost of good Y goes up by 7%:
Demand for both X and Y is cross-price elastic at 3, which means that a rise of 1% in the price of Y causes an increase of 3% in the amount needed of X. Hence, a 7% increase in Y's cost would lead to a 21% decrease in X's quantity requested.
Because the advertising elasticity of demand for X is 4, which means that a 1% decrease in advertising would result in a 4% decrease in demand for X, if advertising falls by 2%, the amount of X that is needed will reduce by 4%. Because of this, if advertising were cut by 2%, the amount of X needed would decrease by 8%.
Demand for X has an income elasticity of -1, meaning that a 1% increase in income results in a 1% decrease in the amount of X that is demanded. Suppose the income increases by 3%. Hence, a 3% increase in income would result in a 3% decrease in the quantity of X demanded.
Question 4:
In the accompanying diagram, point A represents the equilibrium of a customer. Good X is available for $5.
How much does good Y cost?
The consumer buys 30 units of good Y at point A. We can observe from the graph that the price of good Y divided by the price of good X determines the budget line's slope. The budget line's slope is equal to -20, indicating that the cost of good Y is:
Price of Y = -20 = (Price of Y) / 5 -20 * 5 = -100
Therefore, good Y costs $100.
What is the consumer’s income?
At point A, the consumer is spending all of their income on goods X and Y. The equation for the budget line is:
5X + 100Y = Income
Since the consumer is purchasing 30 units of good Y and the price of good Y is $100, the consumer is spending $3,000 on good Y. Therefore, the consumer’s income is:
5X + 100(30) = Income
5X + 3000 = Income
At point A, the consumer is purchasing 10 units of good X. So, the consumer is spending $50 on good X. We can plug this into the equation to solve for income:
5(10) + 3000 = Income
50 + 3000 = Income
Income = $3050
References
Baye, M. R., & Prince, J. T. (2022). Managerial economics and business strategy (10th ed.).
McGraw-Hill Education.
Baye, M. R., & Prince, J. T. (2022). Chapter 4: Supply and Demand. In Managerial economics and business strategy (10th ed., pp. 83-118). McGraw-Hill Education.
Baye, M. R., & Prince, J. T. (2022). Chapter 5: Market Efficiency and Government Intervention. In Managerial economics and business strategy (10th ed., pp. 119-148). McGraw-Hill Education.
Baye, M. R., & Prince, J. T. (2022). Chapter 6: Elasticity. In Managerial economics and business strategy (10th ed., pp. 149-181). McGraw-Hill Education.
Baye, M. R., & Prince, J. T. (2022). Chapter 7: Consumer Choice. In Managerial economics and business strategy (10th ed., pp. 183-214). McGraw-Hill Education.