Microeconomics Answers

As announced in the 2021-2022 National Budget, the Fijian Government is supporting formal and informal sector employees on Viti Levu who are affected by the pandemic through monthly payments of $120 for a period of six months (August 2021 – January 2022). The Fiji Sun dated 23^rd August, 2021 reports “Attorney-General and Minister for Economy yesterday tweeted that: “Days ahead of schedule, we have met the once-in-a-century COVID-19 crisis with one of the largest assistance payouts in history. $72m was paid in unemployment benefits to 200,000 Fijians. In the coming days, we’ll reach 60,000 more bringing the total payout to around $94m.”

Discuss the ways in formal and informal employees benefits from this COVID-19 Unemployment Assistance from the Fijian Government.

Discuss some ways in which the unemployment scheme done by the government benefits the informal and formal employees in Fiji in this pandemic.

What is the law of demand

 Suppose that u(·) is strictly quasiconcave (so that Walrasian demand is single-valued) and differentiable and that the Walrasian demand x(p, w) is differentiable. (a) Show that if u(·) is homogeneous of degree one, then x(p, w) and v(p, w) are both homogeneous of degree 1 in w (with this, the two functions will take the form x(p, w) = wxˆ(p) and v(p, w) = wvˆ(p)). (b) What do the results of previous part imply about the Hicksian demand h(p, u) and the expenditure function e(p, u)? . (c) Show that when x(p, w) is homogeneous of degree 1 in w, for each ` = 1, . . . , L ∂x`(p, w) ∂w w = x`(p, w) (or in matrix form Dwx(p, w)w = x(p, w)). What does this imply about wealth elasticity of demand? (d) Show that when Walrasian demand x(p, w) is homogeneous of degree 1 in w, for each ` = 1, . . . , L X L k=1 ∂x`(p, w) ∂pk pk = X L k=1 ∂xk(p, w) ∂p` pk 2 (or in matrix form p · Dpx(p, w) = Dpx(p, w)p)).

Let X = (−∞,∞) × R L + and assume that the preferences are strictly convex (so that Walrasian demand is signle-valued) and quasilinear. Normalize price of good 1 to be p1 = 1 (a) Show that the Walrasian demand functions for goods 2, . . . , L are independent of wealth w. [Hint: you have to show that when x(p, w) is Walrasian demand at prices p and wealth w, x(p, w) + αe1 is the Walrasian demand at prices p and wealth w + α for any α > −w]. (b) Argue that the indirect utility can be written in the form v(p, w) = w + γ(p) for some function γ(·). [Hint: Recall from the previous assignment that quasilinear preferences can be represented by a utility function that takes the form u(x1, . . . , xL) = x1 + φ(x2, . . . , xL) for some function φ(·).

Consider the utility function u(x) = ; and a standard budget constraint: p₁x₁+p₂x₂=I.

a. Are the preferences convex?

b. Are the preferences represented by this function homothetic?

c. Formally write the utility maximization problem, derive the first order conditions and find the Marshallian demand function.

d. Verify that the demand function is homogeneous of degree 0 in prices and income.

e. Find the indirect utility function.

f. Find the expenditure function by inverting the indirect utility function.

g. Verify that expenditure function E(p; u) is homogeneous of degree 1 in prices.

h. Check if the expenditure function is increasing in each of the prices.