Question

In: Economics

Consider an economy where an agent produces a consumption good with labor.

The agent has the following preferences:

u(c, l) = √c+ α√l

where c is consumption, I is leisure, and a is a parameter. An agent splits her time between labor and leisure such that n +l= 1 where n is how much she works. Prices for the consumption good is p and labor is w. The agent works at a competitive firm (i.e. zero-profit) which transforms labor using the technology

y =F(N) using labor with wage w.

1. Define a competitive equilibrium. You need to include:

.The household problem

.The firm problem

.Market clearing

2. Suppose F(N)= θN. Solve for the optimal c, n, and l.

Expert Solution

According to the question:

1. The household problem:

Households maximize the consumption c and labor n

Firm problem:

Firms try to maximize their profit. The production function is given by:

y = F(N)

Market clearing condition :

The firm is able to sell all its produce.

Y = F(N) =c

2. Firm's problem

Household problem:

Using equation (1) and (2):

Using this equation (3):

l = 1-n

Rahul Sunny answered 2 years ago

Consider an economy that produces output with labor and capital, with those goods allocated to consumption,...

Consider an economy that produces output with labor and capital, with those goods allocated to consumption, investment, and government purchases. Suppose the government very temporarily, and unexpectedly, increases its purchases of goods. (Assume the government finances these temporary purchases by issuing additional debt. Assume the government only purchases goods—it does not produce goods, or employ labor directly.) Explain the impact of this increase in government spending in both the goods and labor markets today. What happens to consumption demand, investment...

(b) Consider an economy where the consumption function is given by ? = 500 + 0.8(?...

(b) Consider an economy where the consumption function is given by ? = 500 + 0.8(? − ?). Investment is given by 2000 − 100? (where ? is the real interest rate), government spending is 5000, taxes are equal to 4000. Exports are 1000, while imports are given by ?? = 0.2?. (i) Suppose that the real interest rate is ? = 5. Calculate the equilibrium level of real GDP for this economy. Now suppose that the Fed decides to...

consider a simple economy that produces only two products: A, B. GOOD A GOOD B Price...

consider a simple economy that produces only two products: A, B. GOOD A GOOD B Price Quantity Price Quantity 2015 20 500 30 500 2016 50 1000 40 500 2017 50 1000 50 1000 Compute nominal GDP, real GDP, and the GDP deflator for each year, using 2018 as the base year.

Consider a buyer and seller who enter into a contract where the seller produces a good...

Consider a buyer and seller who enter into a contract where the seller produces a good and delivers it to the buyer for payment. At the time of making the contract, the seller is uncertain as to the actual cost of the project, and the situation is described by the following: Cost = 30 with probability 60% Cost = 70 with probability 20% Cost = 150 with probability 20% Before production occurs, the seller does learn the cost. The value...

Consider the closed economy Classical model depicted below, where consumption depends positively on disposable income and...

Consider the closed economy Classical model depicted below, where consumption depends positively on disposable income and negatively on the real interest rate. 1) Suppose the government decides to reduce the overall level of taxes. What happens to public savings (Spublic), private savings (Sprivate), and total savings (S)?. 2) ) According to the Classical model, what are the long-run implications of the above change on the real interest rate (r), output (Y), and the expenditure components of output consumption (C), investment...

Consider a small open economy where workers care about their real consumption wage. Assume, in addition,...

Consider a small open economy where workers care about their real consumption wage. Assume, in addition, that the Marshall-Lerner condition holds. This economy starts at the longrun equilibrium and suddenly experiences the following shock. Households get easier access to mortgages and, as a result, the savings rate falls in this economy. What will be the effect of this shock on the medium run equilibrium in this economy? Describe the changes in the equilibrium employment, RER, Trade Balance and real consumption...

Consider an economy where the representative consumer has a utility function u (C; L) over consumption...

Consider an economy where the representative consumer has a utility function u (C; L) over consumption C and leisure L. Assume preferences satisfy the standard properties we saw in class. The consumer has an endowment of H units of time that they allocate to leisure or labor. The consumer also receives dividends, D, from the representative Örm. The representative consumer provides labor, Ns, at wage rate w, and receives dividends D, from the representative Örm. The representative Örm has a...

Consider an economy that employs only labor (L) and produces only food (Y). Draw a diagram...

Consider an economy that employs only labor (L) and produces only food (Y). Draw a diagram that depicts a typical production function for this economy. Describe the two assumptions that give the production function its shape. Draw another diagram of an assumed subsistence line. What does this line represent (as we discussed in class)? Draw a diagram that joins the production function with the subsistence line. Show the expected equilibrium level of labor and output. What would we expect to...

Tax on labor income - Consider a one-period economy where the representative consumer has a utility...

Tax on labor income - Consider a one-period economy where the representative consumer has a utility function u(C;L) over consumption C and leisure L. Assume preferences satisfy the standard properties we assumed in class. The consumer has an endowment of one unit of time. She earns the wage w per unit of labor supplied to the market and has wealth A which yields an interest rate r, so her income is partly coming from labor, partly from capital. Suppose that...

1.Consider a Robinson Crusoe economy. Robinson is a representative agent with utility function:u(c,r)=cr, where c is...

1.Consider a Robinson Crusoe economy. Robinson is a representative agent with utility function:u(c,r)=cr, where c is coconuts, and r is leisure. In order to produce coconuts, technology dictates the production, which is given by c=a√L where a is some constant, and L is labour. Suppose that a=4. Finally, there is a time constraint: r+L=18. Consider a competitive labour market. Given the wage rate, w=2.0, a firm would like to hire units of the labour input. (Answer just the number up...