] Consider a labor market where the demand curve is 𝐻 = 80 − 𝑤 and the supply curve is𝐻 = 𝑤 − 10.(a) [10 marks] Find the market-clearing wage and quantity (measured in number of hours per week per labor forceparticipant). For the next two parts, assume that the market is operating at this wage at the moment.(b) [10 marks] Due to a demand shock, the labor demand curve becomes 𝐻 = 70 − 𝑤. Find the new market-clearing wage and the change in 𝐻.(c) [10 marks] Assume the demand shock as in Part (b). Due to downward wage rigidity, 𝑤 cannot be lower thanthe value found in (a). Find the change in 𝐻.(d) [10 marks] Evaluate the assumption that the supply curve is linear instead of having a vertical (perfectlyinelastic) part. (Limited to 200 words; even if you think that this is a very bad assumption, please use thegiven supply curve for the first three parts.)2
Question
] Consider a labor market where the demand curve is 𝐻 = 80 − 𝑤 and the supply curve is𝐻 = 𝑤 − 10.(a) [10 marks] Find the market-clearing wage and quantity (measured in number of hours per week per labor forceparticipant). For the next two parts, assume that the market is operating at this wage at the moment.(b) [10 marks] Due to a demand shock, the labor demand curve becomes 𝐻 = 70 − 𝑤. Find the new market-clearing wage and the change in 𝐻.(c) [10 marks] Assume the demand shock as in Part (b). Due to downward wage rigidity, 𝑤 cannot be lower thanthe value found in (a). Find the change in 𝐻.(d) [10 marks] Evaluate the assumption that the supply curve is linear instead of having a vertical (perfectlyinelastic) part. (Limited to 200 words; even if you think that this is a very bad assumption, please use thegiven supply curve for the first three parts.)2
Solution
(a) To find the market-clearing wage and quantity, we need to set the demand curve equal to the supply curve and solve for w (wage):
80 - w = w - 10
Solving for w, we get:
2w = 90 w = 45
Substituting w = 45 into either the demand or supply equation, we get:
H = 80 - 45 = 35
So, the market-clearing wage is 45 and the quantity of labor is 35 hours per week per labor force participant.
(b) With the demand shock, the new demand curve is H = 70 - w. Setting this equal to the supply curve and solving for w, we get:
70 - w = w - 10 2w = 80 w = 40
Substituting w = 40 into the new demand equation, we get:
H = 70 - 40 = 30
So, the new market-clearing wage is 40 and the new quantity of labor is 30 hours. The change in H is 30 - 35 = -5 hours.
(c) If w cannot be lower than the value found in (a), which is 45, then the quantity of labor demanded at this wage is:
H = 70 - 45 = 25
So, the change in H is 25 - 35 = -10 hours.
(d) The assumption that the supply curve is linear implies that the quantity of labor supplied increases continuously as the wage increases. This may not be realistic in the real world, as there may be a maximum number of hours that workers are willing or able to work in a week, regardless of the wage. Additionally, the assumption does not account for the fact that the labor supply may be perfectly inelastic (vertical) at low wages, as workers may not be willing to work at all if the wage is too low. Despite these limitations, the linear supply curve is a useful simplification for this analysis.
Similar Questions
The demand curve is 𝐷 =16 − 3𝑝 and the supply curve is 𝑆 = −4 + 2𝑝.(a) [5 marks]Find the competitive equilibrium.(b) [10 marks]Compute the consumer surplus and producer surplus.
The following table models labor supply and demand (in thousands of people).Wage Quantity Supplied Quantity Demanded15 120 13020 130 13525 140 14030 150 14535 160 150Due to COVID-19, the labor demand curve shifts. The new demand can be modeled as follows.Wage Quantity Demanded15 11020 11525 12030 12535 130In the short run, wages are sticky and remain the same as before the pandemic. If the working-age population is 200 thousand and the labor force is 140 thousand, what is the unemployment rate during the pandemic?(Round your answer to one decimal point.)
If producers who hire labourers in a competitive labour market decide to purchase new automated machines that complete the work of 30 employees at once, which of the following is true?Question 4Select one:A.The demand curve for the labour market shifts left.B.The supply curve for the labour market shifts right.C.The supply curve for the labour market shifts left.D.The demand curve for the labour market shifts right.
The demand and supply functions of a good are given by{ P = 7 QD + 18P = −13 QS + 40where P denotes the price, QD the quantity demanded and QS the quantitysupplied.(a) Determine the equilibrium price and quantity.(b) Sketch the demand and supply functions on the same graph. Label theaxes and the intercepts clearly
A manufacturer determines that m employees will produce a total of q units each week. The relation between the number of employees and the quantity is given as: 𝑞 = 5𝑚2 + 2𝑚 + 4. Given that the demand function for the product is given as 𝑝 = 1000 𝑞+8 , determine a. The rate of change of price with respect to quantity b. The rate of change of price with respect to the number of employees c. Determine the marginal revenue when the number of employees is 15
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.