There are many problems in the economic world that have yet to be solved, and fortunately, Wikipedia has compiled a list of the greatest ones to date - from what caused the Industrial Revolution to whether or not money supply is endogenous.
Although great economists like Craig Newmark and members of the AEA have taken a stab at solving these tough issues, the true solution to these problems - that is to say the generally understood and accepted truth of the matter - has yet to come to light.
To say a question is "unsolved" implies that the question potentially has a solution, in the same way 2x + 4 = 8 has a solution. The difficulty is, most of the questions on this list are so vague that they cannot possibly have a solution. Nevertheless, here are the top ten unsolved economic problems.
1. What Caused the Industrial Revolution?
Although there are many factors at play in causing the Industrial Revolution, the economic answer to this question has yet to be sussed out. However, no event has a single cause - the Civil War was not wholly caused by slavery and World War I was not wholly caused by the assassination of Archduke Ferdinand.
This is a question without a solution, as events have numerous causes and determining which ones were more important than others naturally involves some subjectivity. While some might argue that a strong middle-class, mercantilism and the development of an empire, and an easily moveable and growing urban population who increasingly believed in materialism led to the Industrial Revolution in England, others might argue the country's isolation from European continental problems or the nation's common market led to this growth.
2. What Is the Proper Size and Scope of Government?
This question again has no real objective answer, because people will always have differing views on the argument of efficiency versus equity in governance. Even if a population managed to fully understand the exact trade-off that was being made in each case, the size and scope of a government largely depend on its citizenry's dependence on its influence.
New countries, like the United States in its early days, relied on a centralized government to maintain order and oversee rapid growth and expansion. Over time, it has had to decentralize some of its authority to the state and local levels in order to better represent its vastly diverse population. Still, some might argue the government should be larger and control more due to our reliance on it domestically and abroad.
3. What Truly Caused the Great Depression?
Much like the first question, the cause of the Great Depression can't be pinpointed because so many factors were at play in the eventual crash of the United States' economies in the late 1920s. However, unlike the Industrial Revolution, whose many factors also included advances outside of economy, the Great Depression was primarily caused by a catastrophic intersection of economic factors.
Economists commonly believe five factors ultimately resulted in the Great Depression: the stock market crash in 1929, over 3,000 banks failing throughout the 1930s, reduction in purchasing (demand) in the market itself, American policy with Europe, and drought conditions in America's farmland.
4. Can We Explain the Equity Premium Puzzle?
In short, no we have not yet. This puzzle refers to the strange occurrence of returns on stocks being much higher than returns on government bonds over the past century, and economists are still baffled by what could truly be the cause.
Some posit that either risk aversion may be at play here, or antithetically that large consumption variability accounted for the discrepancy in return capital. However, the notion that stocks are riskier than bonds isn't enough to account for this risk aversion as a means to alleviate arbitrage opportunities within a country's economy.
5. How Is It Possible to Provide Causal Explanations Using Mathematical Economics?
Because mathematical economics relies on purely logical constructions, some might wonder how an economist might use causal explanations in their theories, but this "problem" isn't quite that difficult to solve.
Like physics, which can provide causal explanations like "a projectile traveled 440 feet because it was launched at point x from angle y at velocity z, etc.," mathematical economics can explain the correlation between events in a market that follow the logical functions of its core principles.
6. Is There an Equivalent of Black-Scholes for Futures Contract Pricing?
The Black-Scholes formula estimates, with relative accuracy, the price of European-style options in a trading market. Its creation led to a newfound legitimacy of the operations of options in markets globally, including the Chicago Board Options Exchange, and is often used by participants of options markets to predict future returns.
Although variations of this formula, including notably the Black formula, have been made in financial economic analyses, this still proves to be the most accurate prediction formula for markets around the world, so there is still yet to be an equivalent introduced to the options market.
7. What Is the Microeconomic Foundation of Inflation?
If we treat money such as any other commodity in our economy and as such is subject to the same supply and demand forces, reason would suggest it would be just as susceptible to inflation as goods and services are.
However, if you consider this question like one considers the question of "which came first, the chicken or the egg," it may be best left as a rhetorical one. The basis, of course, is that we do treat our currency like a good or service, but where this originates doesn't truly have one answer.
8. Is the Money Supply Endogenous?
Wikipedia follows up this question with a simple statement: "Mainstream economics claims that it is; post-Keynesian economics claims that it is not." However, the issue isn't uniquely about endogeneity, which, strictly speaking, is a modeling assumption. If the question is properly constructed, I think this could be considered one of the key problems in economics.
9. How Does Price Formation Occur?
In any given market, prices are formed by a variety of factors, and just like the question of the microeconomic foundation of inflation, there's no true answer to its origins, though one explanation posits that each seller in a market forms a price depending on probabilities within the market which in turn depends on the probabilities of other sellers, meaning that prices are determined by how these sellers interact with one another and their consumers.
However, this idea that prices are determined by the markets overlooks several key factors including that some goods or service markets don't have a set market price as some markets are volatile while others are stable - all depending on the veracity of information available to buyers and sellers.
10. What Causes the Variation of Income Among Ethnic Groups?
Much like the causes of the Great Depression and the Industrial Revolution, the exact cause of income disparity between ethnic groups cannot be pinpointed to a single source. Instead, a variety of factors are at play depending on where one is observing the data, though it mostly comes down to institutionalized prejudices within the job market, availability of resources to different ethnic and their relative economic groups, and employment opportunities in localities featuring varying degrees of ethnic population density.