Solving ECO 202 Macroeconomics Test 2: Consumption, Unemployment & Investment with Real-World Examples

Understanding the Consumption Model with Taxes

In ECO 202, the consumption model from Chapter 16 is a cornerstone of intertemporal choice. Imagine you're a student in 2026, deciding how much to spend now versus save for future expenses like tuition or a new AI-powered laptop. The utility function U = ln(c) + βln(c') captures your preference for current consumption (c) and future consumption (c'), with β=0.95 meaning you value the future slightly less. With income $15,000 today, $20,000 tomorrow, initial assets $10,000, and an interest rate of 2%, let's build the budget constraint.

Budget Constraints

Current period: c + s = 15,000 + 10,000 - τc (after consumption tax τ). Future period: c' = 20,000 + (1+r)s - τ'c'. Combining gives the lifetime budget constraint: c + c'/(1+r) = 25,000 + 20,000/(1.02) - τc - τ'c'/(1.02). Plugging numbers: c + c'/1.02 = 44,607.84 - τc - τ'c'/1.02. This shows how taxes reduce your purchasing power.

Deriving the Euler Equation

The Euler equation balances marginal utility across periods. From utility maximization, we get 1/c = β(1+r)/c'. With β=0.95 and r=0.02, c' = 0.95*1.02*c = 0.969c. So future consumption is slightly less than current, reflecting impatience.

Optimal Consumption

Solving with the budget constraint (assuming no taxes for now): c + 0.969c/1.02 = 44,607.84 → c = 22,303.92, c' = 21,607.84. With taxes, the optimal levels adjust. For part (d), increasing only current tax τ reduces current consumption and increases savings, lowering c and raising c'. For part (e), smoothing taxes (equal present-value tax) keeps consumption unchanged – a classic result of Ricardian equivalence.

Bathtub Model of Unemployment: Trends in 2026

The Bathtub model describes labor market flows. In 2026, with AI automation and gig economy shifts, understanding separation and finding rates is crucial. The steady-state unemployment rate is u* = s/(s+f) where s is separation rate and f is finding rate. Using the data: 2010: s=0.25%, f=4.5% → u*=0.25/(0.25+4.5)=5.26%. Similarly, 2013: 8.43%, 2015: 6.82%, 2018: 5.71%. The natural rate of unemployment equals the steady-state rate. Employment in each year: E = (1-u*)*L. For 2010: 0.9474*153.9M = 145.8M. If a policy lowers s, u* decreases – for example, job training programs reduce separations. Economists estimate search effort using vacancy data and the Beveridge curve, or via online job search intensity from platforms like LinkedIn, a trend in 2026.

Investment Decision: Kappa Bistro

Kappa Bistro considers buying a stove for $900 at 10% interest, with depreciation 10%. The marginal product of capital (MPK) from production function Y = 24K^{1/2}L^{1/2} is MPK = 12L^{1/2}/K^{1/2}. With L=4, MPK = 24/√K. The user cost of capital = (r+δ)*price = (0.10+0.10)*900 = $180. The additional revenue from one stove: MPK * price per meal = (24/√K)*$24. For K=1 (current), MPK=24, revenue=576, cost=180 → profit. But optimal K equates MPK to user cost: 24/√K = 180/24 = 7.5 → √K=3.2 → K≈10. So buy 9 more stoves? Wait, check: with L=4, diminishing returns. Actually, solve: 24/√K = 7.5 → √K=3.2 → K=10.24, so optimal is 10 stoves. This example mirrors real-world investment decisions in 2026, where restaurants use AI to predict demand and optimize capital.

Key Takeaways

This tutorial covers intertemporal consumption, labor market dynamics, and investment theory – all essential for ECO 202. Use the Euler equation to understand saving behavior in a high-inflation 2026 economy. The Bathtub model helps analyze unemployment in the age of automation. And MPK calculations guide firms in a post-pandemic recovery. Practice with similar problems to ace your test.