y= K∂(AN -ßNß) + CLy (a) Using calculus derive a formula for the aggregate labour demand...

y= K^∂(AN -ßN^ß) + CL^y

(a) Using calculus derive a formula for the aggregate labour demand (N D). Express aggregate labour demand as a function of the real wage w (and all other variables and parameters).

(b) The aggregate quantity of labor supplied is NS = 50 + (1 + s)w, where s is a wage subsidy paid by the government. Assume that s = 1, A = 100, B = 1/4, K = 1, β = 2: solve for the equilibrium real wage (w ∗ ), full-employment level (N∗ ). Assume that L = 10, C = 1 and γ = 2: find the full-employment level of output (Y ∗ ).

(c) The government’s goal is to achieve the employment level N∗∗ = 100: what is the value of the subsidy s ∗∗ that is needed in order to reach this target? What are the implied wage w ∗∗ and output Y ∗∗? Comment on your findings

Expert Solution

Rahul Sunny answered 2 years ago

derive first law of thermodynamics formula with calculus?

Derive the dynamic aggregate demand curve equation.

Derive the aggregate demand curve using both the expenditure function and the MP curve (show these...

Derive the aggregate demand curve using both the expenditure function and the MP curve (show these graphic derivations separately). These two derivations give slightly different representations of the AD curve. Explain the difference.

A firm produces output y using two factors of production (inputs), labour L and capital K....

A firm produces output y using two factors of production (inputs), labour L and capital K. The firm’s production function is ?(?,?)=√?+√?=?12+?12. The wage rate w = 6 and the rental price of capital r = 2 are taken as parameters (fixed) by the firm. a. Show whether this firm’s technology exhibits decreasing, constant, or increasing returns to scale. b. Solve the firm’s long run cost minimization problem (minimize long run costs subject to the output constraint) to derive this...

Graphically derive short run Phillips curve with the help of aggregate demand and supply and demand.

Derive the formula for a (1-α) level confidence interval for the Mean response E(Y|X=x*) using the...

Derive the formula for a (1-α) level confidence interval for the Mean response E(Y|X=x*) using the simple linear regression model, where x* is a specified value for X.

3) Aggregate supply, Aggregate Demand (Use graphs for all your answers) a) Derive the AD curve...

3) Aggregate supply, Aggregate Demand (Use graphs for all your answers) a) Derive the AD curve from the IS-LM model. b) Discuss what affects the slope of the short-run AS and how. Page 3 of 3 c) In the AS-AD model how does a tax cut affect the natural rate of output, the output level, and the level of prices? (Explain both cases of a long-run and a short-run AS curve). d) Discuss the notion of the crowding-out of private...

2.Derive the demand curve for the garment on the y-axis

(i) Derive the Plank's distribution formula. (ii) the way to obtain Plank's constant by using plank's formula.

1a. Derive government spending and tax multiplier in the Keynesian-cross model using calculus 1b. Consider the...

1a. Derive government spending and tax multiplier in the Keynesian-cross model using calculus 1b. Consider the model of Keynesian cross with fixed planned investment expenditure, government spending and taxes. Assume that consumption function is given by C=a+mpc*(Y-T), where the parameter a >0 is called autonomous consumption, and the marginal propensity to consume satisfies 0< mpc <1. Compute equilibrium output (income) as a function of parameters (a and mpc) and exogenous variables. How does equilibrium output depend on a? mpc? Government...

Question