Consider the solution to the problem: maximise 24-z-2-(z-y)² subject to the constraint z+y≤ 3. a) Is it true or false to say the constraint will bind? b) What is the value of x? Please enter an integer or fraction rather than a decimal. c) What is the value of the Lagrangian multiplier on the constraint? Give answer in fraction form

Darwin consumes cigarettes (x1) and other goods (x2). His preferences are given by UD(q1,q2)=4lnq1 +q2The quantity of good 2 is measured in units of income and so you can assume that throughout this problem, the price of good 2 is normalized p2 = 1 (a)  Using the Lagrangian, derive Darwin’s uncompensated demand for cigarettes: D1D(p1,Y). Note that we are holding p2 =1 and so that is not a variable in the demand function. Using the Lagrangian, derive the equation λ∗(p1, Y ). Provide an economic interpretation of the Lagrange multiplier. Does it vary with income, Y ?

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The demand for Good A is Qd = 1000 - 0.5P + 0.011. If, on average, an income increase of 3% increases quantity demanded by 1%, all else constant. Using Qd = 500, how do you write the demand equation?

Laffer curve  In the 1980s, president Reagan based his tax and spending policies on supply side eonomics. The idea behind supply side economics is the marginal tax rate is so high it discourages work. Cutting the tax rate would end up increasing tax revenue. We develop a simple model of this idea to determine the restrictions on the utility function required to generate a Laffer curve. Let T denote the tax rate, w is the real wage rate and n the labor supply. The tax revenue is T=wnT where wn is labor income, which is the tax base. For convinience assume w is constant. There is no reason for this assumption to be true, but we impose it to focus on the restrictions on the utility function to generate the Laffer curve. As the tax rate T increases, workers substitute towards leisure and away from consumption. Hence as T rises, wn falls and tax revenues falls for high enough tax rates. Let U,V satisfy the standard assumptions. The model is static and households are endowed with one unit of…

If the consumer's budget constraint is given by 4P + 2B = 50 where P is Pizza and B is Burgers, the following bundles of Pizza and Burger would be on the budget constraint: P = 5; B = 10 P = 2; B = 21 P = 10; B = 20 %3D P = 2; B = 24