Which economic curve depicts an inverse relationship between the rate of unemployment and the rate of inflation in an economy over the short run?

Introduction / Context:
In macroeconomics, various curves represent relationships between key variables like output, inflation, interest rates and unemployment. The curve that shows a short run trade off between unemployment and inflation is especially important in discussions of stabilisation policy. This question asks you to identify that curve from among several standard diagrams.

Given Data / Assumptions:

• We are looking for a curve that shows an inverse relationship.
• The variables are unemployment and inflation.
• Options include supply curve, indifference curve, IS curve and Phillips curve.
• The context is short run macroeconomic analysis.

Concept / Approach:
The Phillips curve, originally based on empirical work by A. W. Phillips, suggested that when unemployment is low, inflation tends to be high and vice versa, creating a downward sloping relationship in the unemployment inflation space. Although later theory refined this relationship, the basic idea that the Phillips curve shows such a trade off in the short run remains a standard textbook result and often appears in exam questions.

Step-by-Step Solution:
Step 1: Recall that a supply curve usually relates price and quantity of a single good.Step 2: Remember that an indifference curve relates combinations of two goods that give equal satisfaction to a consumer.Step 3: Note that the IS curve relates interest rates and output where the goods market is in equilibrium.Step 4: Identify the Phillips curve as relating inflation to unemployment, typically with a negative slope in the short run.Step 5: Conclude that the curve asked for is the Phillips curve.

Verification / Alternative Check:
Any standard macroeconomics text introduces the Phillips curve with a diagram in which the horizontal axis shows unemployment and the vertical axis shows inflation. The curve slopes downwards from left to right, showing that lower unemployment is associated with higher inflation. The figure is labelled Phillips curve and discussed as a short run policy trade off. This direct association verifies that option D is correct.

Why Other Options Are Wrong:
The supply curve deals with the relationship between price and quantity supplied of a specific good and is not used to relate unemployment and inflation. Indifference curves belong to microeconomics and consumer theory rather than macro level unemployment and inflation questions. The IS curve arises in the IS LM model and shows combinations of interest rates and income where the goods market is balanced. None of these alternatives deals directly with unemployment and inflation together, so they do not answer the question.

Common Pitfalls:
Sometimes students confuse the IS curve with the Phillips curve because both appear in macro models. Another common confusion is to think that any downward sloping curve in macroeconomics could be the Phillips curve. To avoid this, always pay attention to the variables on the axes: unemployment and inflation belong to the Phillips curve, while interest rate and output belong to the IS curve, and price and quantity relate to supply and demand curves.

Final Answer:
The curve that shows an inverse relationship between unemployment and inflation in the short run is the Phillips curve.