mathsperts1

# mathsperts1 - this model the government must collect tax T...

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Economics for Mathsperts I 1. Suppose demand and supply functions are described by q d = a bp q s = c + dp where a; b; c; d > 0 and a > c: Suppose the government imposes a sales tax t > 0 . Find the equilibrium price paid p ( t ) by consumers. Find dp =dt: How does tax incidence depend on the slopes of the supply and demand functions? Illustrate using graphs when demand is perfectly inelastic ( b = 0) or supply is perfectly elastic ( d = 1 ) [unfortunately as economics is a little mad, your graphs must have p on the y-axis]. 2. Repeat the above analysis but for general demand and supply functions. In other words, suppose q d = q d ( p ) and q s = q s ( p ) where q d ( : ) is a decreasing function, q s ( : ) is an increasing function and q d (0) > q s (0) : Find dp =dt and again explain how tax incidence depends on the slopes of the supply and demand functions. Does this more mathematically complex example yield any additional insight? 3. A favourite topic in dodgy macro is the balanced budget multiplier. In
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Unformatted text preview: this model the government must collect tax T to pay for government spending G . Speci&amp;cally a Keynesian equilibrium implies Y; C and T must satisfy the following three equations: Y = C + I + G C = A + m ( Y &amp; T ) T = G where consumption depends on after-tax income Y &amp; T: Note A ; I ; G are numbers (exogenous variable). m is the marginal propensity to consume and satis&amp;es &lt; m &lt; 1 : Using substitution and elimination, solve these three equa-tions for equilibrium Y; C; T as functions of the exogenous variables A ; I ; G : How does an exogenous increase in government spending G a/ect aggregate output Y (with budget balance)? How about a credit crunch which reduces spending A ? Why? 4. Why do I call the above dodgy macro? What was Keynes±defence of this model? Why isn±t m = 1? Think about it. 1...
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