Week 6: Interactive Visualizations

Fig 6.1 Cost Minimisation Sandbox

Set the wage w, rental rate v, and target output q using the sliders. Then drag the dot on the graph to your best guess for the cost-minimising bundle (L, K). The dot turns green when you find the tangency. When you are ready to check your work, click "Show Optimal Bundle" to see the step-by-step solution.

Wage w: 4

Rental rate v: 4

Output q: 3

Fig 6.2 Two-Panel Cost Derivation

Left panel: isoquant map with the expanding isocost sweeping across output levels. Right panel: TC(q) curve building itself point by point. Step through output levels to watch each cost-minimising bundle map to a TC value.

Production function:

Cobb-Douglas production: each input is imperfectly substitutable. The expansion path is a ray through the origin, meaning the firm scales both inputs proportionally as output rises. The TC curve is linear in q (constant returns to scale here).

Isoquant map + isocost

Total Cost curve TC(q)

Fig 6.5 SR vs LR Cost Curves

Short-run Marginal Cost (SMC), Average Variable Cost (AVC), Average Total Cost (ATC), and Average Fixed Cost (AFC) are drawn simultaneously. The Total Fixed Cost (TFC) slider shows how fixed costs shift ATC upward but leave SMC and AVC unchanged. A toggle overlays the Long-Run Average Cost (LRAC) for comparison. All five short-run curve properties in one diagram.

TFC: 100

Fig 6.6 LRAC Envelope Builder

Each SRAC curve corresponds to a different fixed level of capital (K = 1, 2, 3, 4, ...). The LRAC is the lower envelope of all SRAC curves: at each output level, the long-run optimum is whichever fixed-capital option is cheapest. Watch the animation below, then explore the interactive builder.

Interactive builder: drag the slider to add more plant sizes and see the LRAC approach a smooth curve.

Number of SRAC curves: 4

Fig 6.8 Minimum Wage Automation Simulator

Imagine you manage a firm. Currently, the government's minimum wage is exactly what you're paying your workers. Now the government passes a law raising the minimum wage. What do you think happens?

Think about it: if labor suddenly costs more, what would a cost-conscious manager do? Would you use the same amount of labor? Or would you try to use less labor and substitute toward capital?

Use the wage slider below to see the effect. Watch how the isocost line rotates, and see where the new cost-minimising bundle lands. Does it match your intuition?

Min wage w: 3

Capital cost v: 3

Fig 6.10 Efficient Scale Finder

Choose a preset average cost function from the dropdown. The tool plots AC, marks q* (the efficient scale), and shades economies of scale in green and diseconomies in red. Toggle "Show Marginal Cost" to overlay the MC curve and see where it crosses AC at the minimum.

AC function:

Cost Theory